I recently found some references: Theorem 4.5 of <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-4CWYY9T-HT&_user=10&_coverDate=06%2F30%2F1975&_alid=1168943407&_rdoc=1&_fmt=high&_orig=search&_cdi=6838&_sort=r&_docanchor=&view=c&_ct=1&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=80ce7ac14ec803da3335ca133a2221db"> this paper </a> and Theorem 4 + next Corollary of <href="http://www.springerlink.com/content/g48k6345752803mr/"> this paper </a> which says:

If $(R,m,k)$ is a complete normal local domain of dimension $2$ such that $k$ is the algebraic closure of some finite field, then $Cl(R)$ is torsion!

It remains open what happens if $k$ is not algebraically closed.