I have a 560ti and that has a mini HDMI port. With the card when it was purchased was an adapter. Would you have the box from when you got the graphics card? If so, check it.
Otherwise check for an adapter from an online reseller like newegg for an adapter. Depends on length, the
adapters are more expensive than some of the cables. Also check clearance on the back of the card, if that adapter will not work
try this one.
6ft cable starts at $6. Cannot comment on build quality for this but should do the trick.
All the best with sorting it out.