In BioShock Infinite, just prior to the Raffle Square level, there is
a man in a side corner next to the door that the Luteces guard, who
when approached by Booker says “Howdy sailor. What port do you call
home? Any port in the storm…You know what I mean?”. It’s pretty
blatantly a pick up line.

LGBTQ references in this game series:

BioShock (2007): Sander Cohen

BioShock 2 (2010): Brute Splicers 

BioShock Infinite (2013): Guard NPC

BioShock Infinite: Burial At Sea Episode 1: Unnamed Gay Couple 

Citations:

Description and screenshot submitted by Emily R. Foster Brown