Yes, it is possible to switch from a B-1/B-2 visitor visa to an F-1 student visa while in the United States, but you must apply for a change of status with USCIS before your authorized stay expires. You will need to be accepted by a SEVP-certified school, pay the SEVIS fee, and file Form I-539. Importantly, you cannot begin studying until USCIS approves your change of status.