What does "I can get behind that :)" mean when you suggest someone to compromise on an alternative option?

To get behind something is to support it. It is a metaphor that comes from the notion of being physically behind something in order to prop it up.

It doesn't specifically need to refer to a compromise. You can get behind any idea that is proposed.

He found an investor who was willing to get behind his startup company.

See also the related terms backup (n) or back up(v).

I can back up that idea.
I can back that up with sources.
He provided the needed backup for the plan.