The two were photographed while enjoying their coffee together in a balcony in Nashville, Tenn, reported E! Online.
The 27-year-old singer was dressed in a loose-fitting fuchsia dress and the actor was seen sporting a casual look.
Swift first sparked romance rumours with Alwyn last month.
According to the publication at the time, the singer used disguises to go completely unnoticed while getting to know the 26-year-old Joe in the UK.
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