The Collaborative International Dictionary of English v.0.48:

Regidor \Re`gi*dor"\, n.; pl. -dores. [Sp., fr. regir to rule,
   L. regere.]
   One of a body of officers charged with the government of
   Spanish municipalities, corresponding to the English
   alderman.
   [Webster 1913 Suppl.]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

REGIDOR. Laws of the Spanish empire of the Indies. One of a body, never
exceeding twelve, who formed a part of the ayuntamiento or municipal council
in every capital of a jurisdiction. The office of regidor was held for life,
that is to say, during the pleasure of the supreme authority. In most places
the office was purchased; in some cities, however, they were elected by
persons of the district, called capitulares. 12 Pet. R. 442, note.