Yes, you can apply to change from a tourist visa to a student visa, but you must not start school until approved.

You must file Form I-539 with USCIS to change status.

 You must show financial support include bank statements, affidavits, or sponsor letters proving you can pay for school and living expenses.

Do not let your tourist visa expire before USCIS decides, or you risk being denied and removed.

To change from a tourist visa to a student visa, apply for an approved Form I-20, then file Form I-539 with USCIS to request a change of status.