No. US visas may only be granted outside the US. There is an exception for diplomats and for officers and employees of international organizations who are renewing a visa, but that won't help you at all.
The relevant regulation is found at 22 CFR 41.111. It also authorizes the head of the Department of State's visa office to make other exceptions for certain other nonimmigrant categories. I do not know whether such exceptions have been made, but even if they have, they may not include first-time visa applicants, and F is not among the eligible categories:
§ 41.111 Authority to issue visa.
(b) Issuance in the United States in certain cases. The Deputy Assistant Secretary for Visa Services and such officers of the Department as the former may designate are authorized, in their discretion, to issue nonimmigrant visas, including diplomatic visas, to:
(1) Qualified aliens who are currently maintaining status and are properly classifiable in the A, C-2, C-3, G or NATO category and intend to reenter the United States in that status after a temporary absence abroad and who also present evidence that:
(i) They have been lawfully admitted in that status or have, after admission, had their classification changed to that status; and
(ii) Their period of authorized stay in the United States in that status has not expired; and
(2) Other qualified aliens who:
(i) Are currently maintaining status in the E, H, I, L, O, or P nonimmigrant category;
(ii) Intend to reenter the United States in that status after a temporary absence abroad; and
(iii) Who also present evidence that:
(A) They were previously issued visas at a consular office abroad and admitted to the United States in the status which they are currently maintaining; and
(B) Their period of authorized admission in that status has not expired.