It really depends on where you go, what the core curriculum is like, and your major. My daughter, who attends a selective LAC (and did not take Calc), satisfied her quantitative requirement with her AP Stats score. Her college has a fairly flexible and minimal set of core requirements. Had she not used the AP score, she could have satisfied the requirement with stats or even a particular philosophy class that focuses on logic, and then would have had to take nothing more that was math-related. She, like OP, is a humanities person – this wouldn’t have worked with a STEM major.
So it can be done, and at quite a few schools, too, including selective schools with open curricula. Many selective schools do want to see four years of math in HS, though, so if you don’t want to take Calc AB, you might consider other math electives for your senior year, if available. Fair warning - some will want to see Calc AB. But many just want four years of math.