A swag shirt is a button up shirt with a collar, usually with the sleeves rolled up., This is often worn at formal events/parties when you want to "keep your swag".
Hayden: "dude are you ready for the party tomorrow?!"
John: "hell yeah! i got my swag shirt at home ready to go!"
"Man i have to go to the mall to buy a new swag shirt."
"Crap i got wine spilled all over my favorite swag shirt!"