The MPAA is the Motion Picture Association of America. Their site says this (emphasis mine)
Established in 1968, the film rating system provides parents with the information needed to determine if a film is appropriate for their children.
In other words, the MPAA rates movies. Star Trek TOS was television, which would not be rated until 1997, and not by the MPAA
On December 19, 1996, the industry announced the creation of the TV Parental Guidelines, a voluntary system of guidelines providing parents with information to help them make more informed choices about the television programs their children watch. The guidelines were modeled after the movie ratings system created by the Motion Picture Association of America in 1968. The television industry agreed to insert a ratings icon on-screen at the beginning of all rated programs, and to encode the guidelines for use with the V-chip. The industry also created a Monitoring Board, composed of TV industry experts, to ensure accuracy, uniformity and consistency of the guidelines and to consider any public questions about the guideline applied to a particular program. The TV Parental Guidelines went into use on January 1, 1997.
Retroactively, the TOS episodes have been rated TV-PG (all the ones on IMDB say TV-PG but I was not exhaustive in looking).
Interestingly enough, the first Star Trek to get a true MPAA rating would be Star Trek: The Motion Picture (1979), which is rated G. The Director's Cut is rated PG.