“Rapture” itself is NOT a Bible word,

but the concept is Scriptural. The New Oxford American Dictionary tells us,

“noun

“1 a feeling of intense pleasure or joy: Leonora listened with rapture. …

“2 (the Rapture) N. Amer. (according to some millenarian teaching) the transporting of believers to heaven at the Second Coming of Christ.”

Actually, “transporting of believers to heaven at the Second Coming of Christ,” is not just a premillenial belief, but is held by most who believe the Bible

“16 For the Lord himself will descend from heaven with a shout, with the voice of the archangel, and with God’s trumpet. The dead in Christ will rise first, 17 then we who are alive, who are left, will be caught up together with them in the clouds, to meet the Lord in the air. So we will be with the Lord forever. 18 Therefore comfort one another with these words.”
1The 4:16-18

At the Second Coming of Christ,

“30 and then the sign of the Son of Man will appear in the sky. Then all the tribes of the earth will mourn, and they will see the Son of Man coming on the clouds of the sky with power and great glory. 31 He will send out his angels with a great sound of a trumpet, and they will gather together his chosen ones from the four winds, from one end of the sky to the other.”
Mtt 24:30-31

And there are various other episodes of people being caught up to God. In 2Kings chapter two Elijah is caught up to heaven in a fiery chariot. The apostle Paul, seemingly speaking of himself, tells of someone being “caught up” to “the third heaven,” to “Paradise.”

“2 I know a man in Christ, fourteen years ago (whether in the body, I don’t know, or whether out of the body, I don’t know; God knows), such a one caught up into the third heaven. … 4 how he was caught up into Paradise, and heard unspeakable words, which it is not lawful for a man to utter.”
2Cor 12:2, 4

Of course Jesus Himself was caught up to heaven.

“9 When he had said these things, as they were looking, he was taken up, and a cloud received him out of their sight. 10 While they were looking steadfastly into the sky as he went, behold, two men stood by them in white clothing,”
Acts 1:9-10

And Jesus was returning to heaven so that He could go beyond all of our universe.

“9 Now this, “He ascended,” what is it but that he also first descended into the lower parts of the earth? 10 He who descended is the one who also ascended far above all the heavens, that he might fill all things. ”
Eph 4:9-10

This is described as being “caught up” in Revelation 12.

“She gave birth to a son, a male child, who is to rule all the nations with a rod of iron. Her child was caught up to God, and to his throne.”
Rev 12:5

But there are other issues.

Scriptures are from the World English Bible WEB, a copyright free revision
of the original ASV American Standard Version 1901.