It is “improvisor”. Even though both Google and Answers.com say otherwise.
From the following site: The Un-Scripted Theater – Company Store. Although, they need to think about how to spell theatre.
‘-or’ and ‘-er’ are noun suffixes denoting an agent or doer; as in auditor, one who hears; donor, one who gives; obligor; elevator. It is correlative to ‘-ee’. In general ‘-or’ is appended to words of Latin, and ‘-er’ to those of English, origin.
French ‘improvisor’, from Italian ‘improvvisare’, from ‘improvviso’, unforeseen, from Latin ‘imprvisus’ : in-, not; see in+ ‘provisus’, past participle of ‘providere’, to foresee.
Therefore, to ‘improvise’, from the Latin ‘improvidus’, would thus dictate the use of the Latin ‘-or’ suffix, and thus make those who practice the art of improvisation improvisors!