I found this database online: Socorro County, New Mexico Marriages 1727-1900. Although the title says that the list is from 1727-1900, it's actually from the mid 1860 to the late 1880s.
This is just one of the databases on Socorro to be found on the Genealogy Trails History Group. Other records found on this site include census transcriptions, biographies, military data and history.
As with any online resource, always be careful. Do not accept it as a source for your research. Rather, use it as a clue to find more reliable information. This is especially important since the database does not cite a source. I have no idea where it came from. It's possible that it was found in either the San Miguel Church or the Socorro County marriage records.