Can I transfer my current domain and upload my web site?
You meaning of transfering is to use your own domain on x10 hosting account?
Yes, You can use your own domain, Just change the nameservers to
ns1.x10hosting.com
ns2.x10hosting.com
The DNS propagation may take upto 48 hours.
Then
Make the domain as your primary domain in your account panel
OR
Park the domain in your cpanel