You could try and file for a change of status to F-1 or depart the US to apply for a new visa once you have an I-20. Consult with an immigration attorney ASAP to plan the next step.
There may be ways. However, there is a lot more information needed and the legal advice you need may not be suitable for this forum. You should consult with an attorney in person and get a full legal advice.
Ismail T. Shahtakhtinski, Esq.
Attorney & Counselor at Law
I.S. Law Firm, PLLC
1199 N Fairfax St., Ste 702
Alexandria, VA 22314
Tel: (703) 527-1779
Fax: (703) 778-0369
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By leaving the US, applying for the F-1 visa stamp abroad and returning to start your studies.
The Court of Appeals for the Seventh Circuit recently stated: "The Immigration and Nationality Act is a bit of a beast. It is not known for being warm or cuddly; words like "intricate" and "Byzantine" come more readily to mind. Nor is it known for being easy to understand; we have often re-marked on its fiendish complexity."
You should retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
The statement above is general in nature and does not constitute legal advice. Legal advice cannot be provided through a forum such as this. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.