According to E! online the singer used disguises to go completely unnoticed while getting to know 26-year-old Joe in the UK.
Joe made his feature film debut opposite Kristen Stewart, Vin Diesel, Garret Hedlund and Steve Martin in 2016's "Billy Lynn's Long Halftime Walk".
Around the time of its release last November, Swift, 27, was spotted at a Hollywood screening for the war drama with her mom and a group of friends.
Swift's latest romance follows her highly-publicised relationship with Tom Hiddelston, which came to an end last September.
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