Depends how high and where you built it!
If you built one on the equator, standing at the top you'd be whizzing around at a fair old rate as you'd be following the earth's rotation, so in theory, yes it's possible.
If you built one on one of the poles you'd have to get a veeeeery long way away as earth's gravity would still be pulling you down, albeit with a tiny amount of force, but given long enough you'd eventually get pulled back to earth. (unless you were so far away that another planet/star was pulling harder)
The key is to have a rotational velocity, which in turn will give you the acceleration to overcome gravity.
(apologies for not necessarily using the correct terms, it's been a few years since physics!)