Johnny Cash sang a song (2002) called Personal Jesus; originally
performed by the group Depeche Mode
Catholics have this same relationship in their own way, couched in different terms, and Catholicism teaches its adherents to renew their commitment to God not just once in an "altar call" but daily (hence the daily Mass).
The Imitation of Christ was written by Thomas à Kempis (c. 1380 – 1471). He died before Protestantism began (around 1517). This book is typical of many dozens of such meditations by pious Catholics and Catholic mystics through the ages. Here are but a few portions that would relate to the question of a “personal relationship with Jesus,” as many Protestants would put it. This communion with God is not at all foreign to authentic Catholic practice and tradition and devotion:
The kingdom of God is within you,” says the Lord. [Luke 17:21]
Turn, then, to God with all your heart. Forsake this wretched world and your soul shall find rest. Learn to despise external things, to devote yourself to those that are within, and you will see the kingdom of God come unto you, that kingdom which is peace and joy in the Holy Spirit, gifts not given to the impious.
Christ will come to you offering His consolation, if you prepare a fit dwelling for Him in your heart, whose beauty and glory, wherein He takes delight, are all from within. His visits with the inward man are frequent, His communion sweet and full of consolation, His peace great, and His intimacy wonderful indeed.
Therefore, faithful soul, prepare your heart for this Bridegroom that He may come and dwell within you; He Himself says: “If any one love Me, he will keep My word, and My Father will love him, and We will come to him, and will make Our abode with him.” [John 14:23]
Give place, then, to Christ, but deny entrance to all others, for when you have Christ you are rich and He is sufficient for you. He will provide for you. He will supply your every want, so that you need not trust in frail, changeable men. Christ remains forever, standing firmly with us to the end.
. . . you shall have no rest until you are wholly united with Christ.
. . . Fix your mind on the Most High, and pray unceasingly to Christ.
. . . Had you but once entered into perfect communion with Jesus or tasted a little of His ardent love, you would care nothing at all for your own comfort or discomfort but would rejoice in the reproach you suffer; for love of Him makes a man despise himself.
A man who is a lover of Jesus and of truth, a truly interior man who is free from uncontrolled affections, can turn to God at will and rise above himself to enjoy spiritual peace.
(Book II: The Interior Life, chapter one: “Meditation”)
Blessed is he who appreciates what it is to love Jesus and who despises himself for the sake of Jesus. Give up all other love for His, since He wishes to be loved alone above all things.
Affection for creatures is deceitful and inconstant, but the love of Jesus is true and enduring. He who clings to a creature will fall with its frailty, but he who gives himself to Jesus will ever be strengthened.
Love Him, then; keep Him as a friend. He will not leave you as others do, or let you suffer lasting death. Sometime, whether you will or not, you will have to part with everything. Cling, therefore, to Jesus in life and death; trust yourself to the glory of Him who alone can help you when all others fail.
Your Beloved is such that He will not accept what belongs to another—He wants your heart for Himself alone, to be enthroned therein as King in His own right. If you but knew how to free yourself entirely from all creatures, Jesus would gladly dwell within you.
You will find, apart from Him, that nearly all the trust you place in men is a total loss. Therefore, neither confide in nor depend upon a wind-shaken reed, for “all flesh is grass” [Isaiah 15:6] and all its glory, like the flower of grass, will fade away.
You will quickly be deceived if you look only to the outward appearance of men, and you will often be disappointed if you seek comfort and gain in them. If, however, you seek Jesus in all things, you will surely find Him. Likewise, if you seek yourself, you will find yourself—to your own ruin. For the man who does not seek Jesus does himself much greater harm than the whole world and all his enemies could ever do.
(Book II: The Interior Life, chapter seven: “Loving Jesus Above All Things” [complete] )
When Jesus is near, all is well and nothing seems difficult. When He is absent, all is hard. When Jesus does not speak within, all other 66 comfort is empty, but if He says only a word, it brings great consolation.
Did not Mary Magdalen rise at once from her weeping when Martha said to her: “The Master is come, and calleth for thee”? [John 11:28] Happy is the hour when Jesus calls one from tears to joy of spirit.
How dry and hard you are without Jesus! How foolish and vain if you desire anything but Him! Is it not a greater loss than losing the whole world? For what, without Jesus, can the world give you? Life without Him is a relentless hell, but living with Him is a sweet paradise. If Jesus be with you, no enemy can harm you.
He who finds Jesus finds a rare treasure, indeed, a good above every good, whereas he who loses Him loses more than the whole world. The man who lives without Jesus is the poorest of the poor, whereas no one is so rich as the man who lives in His grace.
It is a great art to know how to converse with Jesus, and great wisdom to know how to keep Him. Be humble and peaceful, and Jesus will be with you. Be devout and calm, and He will remain with you. You may quickly drive Him away and lose His grace, if you turn back to the outside world. And, if you drive Him away and lose Him, to whom will you go and whom will you then seek as a friend? You cannot live well without a friend, and if Jesus be not your friend above all else, you will be very sad and desolate. Thus, you are acting foolishly if you trust or rejoice in any other. Choose the opposition of the whole world rather than offend Jesus. Of all those who are dear to you, let Him be your special love. Let all things be loved for the sake of Jesus, but Jesus for His own sake.
Jesus Christ must be loved alone with a special love for He alone, of all friends, is good and faithful. For Him and in Him you must love friends and foes alike, and pray to Him that all may know and love Him.
Never desire special praise or love, for that belongs to God alone Who has no equal. Never wish that anyone’s affection be centered in you, nor let yourself be taken up with the love of anyone, but let Jesus be in you and in every good man. Be pure and free within, unentangled with any creature.
You must bring to God a clean and open heart if you wish to attend and see how sweet the Lord is. Truly you will never attain this happiness unless His grace prepares you and draws you on so that you may forsake all things to be united with Him alone.
When the grace of God comes to a man he can do all things, but when it leaves him he becomes poor and weak, abandoned, as it were, to affliction. Yet, in this condition he should not become dejected or despair. On the contrary, he should calmly await the will of God and bear whatever befalls him in praise of Jesus Christ, for after winter comes summer, after night, the day, and after the storm, a great calm.
(Book II: The Interior Life, chapter eight: “The Intimate Friendship of Jesus” [complete] )