It seems pretty popular to think so, but I can't find any passage in the bible that says so.
A quick internet search revealed the following answer:
Premarital Sex
So I looked up 1 Corinthians 7:2. Turns out there is nothing in there about sex before marriage. Paul suggests that getting marred might be a good way to avoid sexual immorality, but that doesn't mean that all sex before marriage is a sin.
Married guys might be a bit less inclined to have sex with their sheep for example. This being the case, marriage would still be a "cure" as described.
In fact, the bible does a pretty good job of defining sexual immorality for us, so we don't really need to guess. It contains a comprehensive and exhaustive list of sexually immoral acts in Leviticus 18.
Leviticus 18 - Passage*Lookup - New International Version - BibleGateway.com
Conspicuously absent from this extremely detailed list, is sex with women who are unmarried.
In fact, to my knowledge, there are only two verses in the entire bible that address sex with unmarried women at all. They are found in Exodus 22:16-17
Exodus 22:16-17 - Passage*Lookup - New International Version - BibleGateway.com
So if a dude has sex with an unmarried virgin who isn't already pledged to be married, he has to offer to marry her. If the father refuses, he still has to pay the bride price as if he were going to marry her.
As a measure of comparison, working on Saturday gets you killed.
Exodus 31:15
Having sex with unmarried women who aren't virgins comes with no penalty at all. having sex with a virgin to whom you are already betrothed comes with no penalty. Girls having sex with dudes who are unmarried virgins or otherwise doesn't appear to either.