Is it possible to have round ligament pain when not pregnant?

Yes,: Yes, especially if the uterus is significantly enlarged, a large ovarian cyst is present or if adhesions are also present.

Possible, unlikely: While it is certainly possible to have similar pain as round ligament pain despite not being pregnant, i doubt the pain in question is "round ligament" pain because as far as i know, round ligament pain is only diagnosed in pregnant women. Thus, if your current pain persists or worsens, it is worth contacting your health care provider.