I have had a floater in my eye for over a week. Is there any known way to get rid of it?

Yes! This can be a result of the normal aging process in the vitreous (jelly in the eye). You need an eye exam to make sure this is not a tear or hole in the retina. Typically you should wait for at least a year to see if it will subside or stop bothering you on its own. If not you can have surgery to remove the floater (vitrectomy).