Short Answer : Yes
But what do you mean by "will fit in my desktop"? Do you mean the physical size? Or the compatibility?
The first long slot on your motherboard is your PCI-E x16 slot, there is where you insert your graphic card.
You would probably need a Good Brand 300W PSU, or any 500W Power Supply.
I have myself a HD 7770, and I can tell you its a great card!
-Hope it helps!