。
It's on me.
Literal
I [of-の] treat is [emphasis-よ].
おごり is the noun form of 奢る ('to treat [someone], to be extravagant'). 僕のおごり = 'my treat.' A classic restaurant phrase. Japanese frequently uses noun forms of verbs in place of full verb predicates: 買い物 ('shopping'), 遊び ('play'), おごり ('treat').