Believe it or not, one of my cats does that too. Bandit steals my bras and takes them around the house at night, meowing pitifully the whole time. I never know where my bra will be the next morning.
I let her do it. If it annoyed me, I'd put them away in a drawer... but she just enjoys it so much!
I caught my boys playing tug of war out in the yard one time with a piece of white material. On closer examination, it was a pair of my panties. I have a cat who likes to raid the laundry basket and particularly likes panties and bras. He would drag them downstairs to where the dogs stay and obviously the dogs found them and brought them outside to play.
My Simba was a Bra Bandit when he was around 6 months old.....he'd run in the bathroom while I take a shower, grab the bra, and run like hell with it! Never did understand what was so fun about running with a bra trailing behind him but he got a real charge out of it. At 9 years old now, he's matured past those silly antics but I sure love remembering that