Yes, you can! I've been wanting to do this one for a long time but haven't been in the Xi'an area since I found out about it!
Hua Shan is about 80 miles from Xi'an in Shaanxi province. There is a regular bus from Xi'an, or you can take a taxi although that will obviously cost more.
From all of the accounts I've read, as long as you're not afraid of heights, and as long as you've done at least a little of "semi-extreme" hiking then you'll have no problems completing the climb.
Mind you, if you'd prefer not to do the climb then you can always just take the cable car to the top!