Can a person take theatre tickets?

I'm not sure this is what you're asking.

A person would usually buy theatre tickets.

An usher in a theatre would take the ticket from the patron.

I agree with Lewis that your sentence is ambiguous. I would add a couple other possibilities, depending on the context:

(1) He took the theatre tickets = He stole the theatre tickets.

(2) With some additional information foregrounded and perhaps added after:   Father left the house this morning, and he took the theatre tickets with him.  He will meet us at the theatre tonight.