Upvote:4
There is a way to change your status, but depending on where you are it might be less expensive to leave and come back. The filing fee is currently $370, and the form to file is I-539. Depending on the timing, you might need to file a separate extension of status application (see Change of Status at DHS and B1/B2 visa change status to F1 (2018). Need advice? on Expatriates). This uses the same form and requires payment of another $370 fee.
It will certainly be quicker to leave and come back, and if you are in the US in B-1 or B-2 status you aren't allowed to undertake your program of study, so you'll be stuck doing nothing while the application is pending. This can take several months, and, as noted on the DHS page, it could require you to defer your studies.
Since you already have the F-1 visa, it's probably better to take a quick road trip or even a flight to Canada or Mexico. Then your application to enter the US in F status will be decided at the border when you return, in a few minutes.