Is trustworthy a verb

No, trustworthy, meaning "worthy of trust", is an adjective.

A verb would be "trust", as in "to trust somebody".

A verb is a Word that describes an action (run, walk, etc), a state of being (exist, stand, etc) or occurrence (happen, become, etc).

An adjective is a Word that describes a noun (the car is blue / it was a cold day / etc).