I have 2 ground wires that I can get around the ground screw on an outlet. Is it okay to do this or do I need to use a pigtail to join the wires and have only one wire attach to the ground screw?
In all my years I have never seen a device ground screw rated for two conductors. Even clamp type ground connectors found on GFI devices are only rated for one conductor.
You will need to pigtail a single wire to the device. This can be achieved several ways. A green wire nut, a ground crimp, or a standard wire nut are examples.
The reason that wiring devices have grounding connections that accept only one wire is that otherwise, if two ground wires were connected to the device, then if someone later removed that wiring device and then re-applied power without wire-nutting the grounding conductors, there would be a break in the ground path for the downstream wiring but perhaps not the hot wires.
Most screw terminals are designed for only a single wire.
No you can't.
You must be able to remove devices without severing ground
If two ground wires went to a device, like they do with hots on receptacles, then if you remove the receptacle (say for servicing), you cut that ground to downstream appliances. Thanks to MWBCs and the retrofit rules, it's possible that ground may serve things that are not on this breaker. You must pigtail it - always with grounds!
In fact, MWBCs have the same rule for neutrals - "pigtail it, mustn't sever neutral for downline appliances". That's because older MWBCs are on separate breakers, and that neutral could be returning current for another breaker that you didn't think to turn off. (this is why MWBCs currently require a "common maintenance shutoff" breaker).