A warm welcome to Mac-Forums, mlp48
Yes, a bit more info would help; such as the Operating system on your Mac and the model of the Mac.
A trivial point about terminology, just for my clarification; I presume you meant the Contacts icon in your Dock (at the very bottom of the screen) rather than your Desktop?
As our Admin chscag said, if your contacts are on your iPhone and in iCloud, as you state:
On your Mac, Open System Preferences > iCloud and make sure that Contacts is checked along with any other things you want synced between devices.
Of course, you have to be signed into iCloud on the iPhone and on the Mac for syncing to happen.
Please post back. We are here to help.
Ian