Stanrick is a pairing between the two protagonists of Gravity Falls and Rick and Morty Stan Pines and Rick Sanchez respectively. Though many see it as more of a friendship or simply a business partnership, there's still a large group of fans who enjoy the idea of them being together romantically.
Because the two exist in completely different shows (multiverse aside), this means that the two have not met, at least that we've seen. Naturally this hasn't stopped a large number of fans from supporting this ship.
Various fans have noted that the two characters share several similarities particularly when it comes to their criminal tendencies. Many fans have theorised that Rick was once a business associate of Stan's in some scam and that the two may've done time together in the Columbian prison where Rick eventually escaped or was released abandoning Stan in the process.