No, you cannot file Married Filing Jointly if you were not married on 12/31/2016.
Not married on 12/31/16 means not married for all of 2016 for tax purposes. The same concept would apply if you were unmarried for most of the year, then got married at the end of the year. Your status on just 1 day determines an entire year.
Your options are Single or Head of Household (if a qualifying child lives with you).