I'm lawfully married to a U.S citizen here in the states in July 2018 but I don't have a Social Security Number yet. Can she add my name when filing her tax returns?.

[Leonard]

Your spouse can not add you to her tax return unless you have a Social Security Number or an ITIN.  Your spouse can file an extension to file the tax returns while you are waiting for your ITIN or SSN whichever one you have applied.  When you receive the number then your spouse can add you to the tax return.