I looked on A Wiki of Ice and Fire but it didn't say. I know Mors Martell married Nymeria, a Rhoynar, and Dornishmen have Rhoynar blood in them. But what was Mors Martell's, and all of Dorne's, ancestry before then? Were they First Men or Andals? Had the Andals even invaded when Nymeria came over?
He was almost certainly an Andal.
By the time Nymeria and the Rhoynar arrived in Westeros, the Andals have been there for at least 1000 years. By that time, the Andals have pretty much driven the First Men north, which is why you find descendants of the First Men mostly in the North and a few in the Vale and the Riverlands. When Nymeria arrived, Dorne was a fractured region with several Andal kingdons fighting for dominance. It was when Mors Martell married Nymeria and allied himself with the Rhoynar that he became strong enough to conquer all of Dorne.
House Martell was founded by Morgan Martell who is referred to as an Andal.
And on the eastern shore, between the Broken Arm and the Greenblood, an Andal adventurer named Morgan Martell and his kin descended on lands loosely held by House Wade and House Shell, defeated them in battle, seized their villages, burned their castles, and established dominion over a strip of stony coastlands fifty leagues long and ten leagues wide.
Over the centuries that followed, their strength grew...but slowly, for then and now the lords of House Martell were renowned for their caution. Until the coming of Nymeria, no Dornishman would ever have counted them amongst the great powers of the country. Indeed, though surrounded by kings on every side, the Martells themselves never presumed to claim that title, and at certain points in their history, they willingly bent the knees to the Jordayne kings of the Tor, the pious Allyrions of Godsgrace, the many petty kings of the Greenblood, and the mighty Yronwoods of Yronwood.
The World of Ice and Fire, Dorne: The Andals Arrive
As Mors Martell is a descendant of Morgan and I find no reference to them marrying outside of Andals until Mors marries Nymeria I think it's likely he was an Andal.