There is nothing precisely equivalent to the notion of semantic roles, or 'thematic roles', in the Indian tradition. The closest categories are the kārakas, but these are more abstract grammatical categories than semantic categories. See the entries 'Argument structure' and 'Subjecthood'.
The kāraka kartṛ is argued to be equivalent to a notion of the most proto-agentive role in the entry 'Subjecthood'.
On the relation between the kāraka karman and the semantic roles of Patient and Theme, see the entry 'Objecthood'.