Acting is not an occupation that is recommended for any of the Varnas. Not even recommended for any of the mixed castes.
Manu Smriti 10.80. Among the several occupations the most commendable
are, teaching the Veda for a Brahmana, protecting (the people) for a
Kshatriya, and trade for a Vaisya.
Similarly from the Parashara Smriti's Chapter 1:
A king of the Kshatriya caste should arm himself,and have his troops ; should protect his people ; should overcome the forces of a
hostile king ; and rule the State in the way prescribed by law.
To invest money on interest, to be a jeweller, to tend cattle, tillage and trade, — these are declared as occupations for the Vaisya
The highest virtue for a Shoodra is to serve the members of the regenerate castes. Fruitless for him is everything else that he may
So, we can't say what is THE Varna of anyone who by profession is an actor.
Actors are always condemned as degraded in the Smritis. So, acting hasn't been recommended as a suitable occupation for any Varna.
Manu Smriti 4.214. Nor the food (given) by an informer, by one who
habitually tells falsehoods, or by one who sells (the rewards for)
sacrifices, nor the food (given) by an actor, a tailor, or an
8.102. Brahmanas who tend cattle, who trade, who are mechanics, actors (or singers), menial servants or usurers, the (judge) shall treat like
The following verse is quoted by Madhava while commenting on one verse of the Parashara Smriti. It regards actor to be one of the lowest castes.
Washerman, cobbler, actor, Varuda, Kaivarta, Meda and Bhilla, these
seven are described in the Smriti as lowcastes. (3)
Angiras Smriti, Chapter 1.