Can I apply for F1 visa after being deported 2 months ago because of the difference between ds160 and the visa I use to enter USA?

If you have been deported, you cannot return to the US unless you have advance permission from USCIS to return or you have served out the period of time required by law for your deportation. That applies for any type of visa, including F-1. If you believe that you have a sympathetic case, you can apply for the F-1 and upon being refused, ask the consular officer to recommend to DHS that you be given a temporary waiver to enter the country. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.