It depends what you want to protect.
If you just want to protect that outlet then it's easy. Pigtail the Black and white wires and connect them to the feed side of the GFCI. Leave the load side of the GFCI disconnected.
Where it gets tricky is if you want to also protect downstream outlets. Current that flows out through a GFCI must return through the same GFCI. Otherwise it will trip. So to protect both hots using GFCI outlets you would need two such outlets and you would need to keep the neutrals downstream of the GFCIs seperate which would likely require some rewiring.
An alternative may be to use a double pole GFCI breaker at the panel.
Another alternative is just to install a seperate GFCI at each outlet.
