。
Want to go see a movie with me?
Literal
I [to-に] together movie [object-を] see [purpose-に] go [question-ないか].
The invitation pattern ~ないか ('won't you...?') combined with the casual purposive 見に行く ('go to see'). 一緒に = 'together.' The 僕に at the start is unusual — typically 僕と would be expected, but 僕に 一緒に is a colloquial variant implying the speaker as the focal co-participant.