I just checked the status of double tax treaties between Cyprus and a few other countries and from what I found it seems that the US has signed one. read below:
http://www.mondaq.com/cyprus/x/291284/Corporate+Tax/Eligibility+For+Benefits+Under+The+USCyprus+Double+Tax+Convention+And+The+Reduced+US+Tax+Rate+On+Dividends+From+Qualified+Foreign+Corporations
http://www.mondaq.com/cyprus/x/291284/Corporate+Tax/Eligibility+For+Benefits+Under+The+USCyprus+Double+Tax+Convention+And+The+Reduced+US+Tax+Rate+On+Dividends+From+Qualified+Foreign+Corporations