Yes you can buy a Y fitting, that fits the male garden hose (onto existing hot & cold faucets for washer), and provides two outlets, one for the washer and the other for the sink. If you look around they are available with built-in shut-offs in the branches.
Then you will need two 3/4" Male garden hose X 1/2"Female Iron Pipe Size. This will fit onto the faucet 1/2" M.I.P.
Also purchase two Automatic Washer supply hoses, to go from the faucet to one side of the Y fitting.
Perhaps you would want to upgrade and purchase the stainless steel braided supply hoses.