How do i get my design on a t-shirt without using a print-out paper transfer?

(im no good at painting and i dont have the right materials to do that anyways) i have a really good idea for a t-shirt design that i want to put on a kind of off-white polyester tshirt. the problem is, i dont want the design to be stiff like it would be by using a paper transfer. are there any companies i could send in my picture and theyd print it on my tshirt without it changing the texture of the fabric?