While you can make many free crochet bag patterns using acrylic yarn, most crocheters don't recommend it. Cotton yarn is more durable and less stretchy than most acrylic yarns.  If you' don't want to use a 100% cotton yarn, I'd recommend going with some sort of cotton blend. You'll find that an acrylic bag is less likely to keep its shape.  If you do feel like you'd definitely like to use acrylic yarn, try to find one that's not stretchy (Caron Simply Soft comes to mind).