I did not enter with a visa but surrendered myself at the border on arrival. Does it mean I did not enter legally?Am married to a US Citizen. Can I?

The answer depends upon what the Department of Homeland Security did with you at the time that you surrendered yourself at the border upon arrival. If you were processed regularly, you did not enter legally. If you were paroled into the U. S. either at the border or after being detained, you might be considered eligible for adjustment of status. Otherwise you may wish to seek other relief and perhaps meet with an immigration lawyer to see whether you are eligible for something like the I-601A program. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (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.