Why no. He absolutely was NOT!
King was not a partisan and never endorsed any political candidate. In a 1958 interview, King said “I don’t think the Republican party is a party full of the almighty God nor is the Democratic party. They both have weaknesses … And I’m not inextricably bound to either party.”
King did, however, weigh in on the Republican party during his lifetime. In Chapter 23 of his autobiography, King writes this about the 1964 Republican National Convention:
The Republican Party geared its appeal and program to racism, reaction, and extremism. All people of goodwill viewed with alarm and concern the frenzied wedding at the Cow Palace of the KKK with the radical right. The “best man” at this ceremony was a senator whose voting record, philosophy, and program were anathema to all the hard-won achievements of the past decade.
Senator Goldwater had neither the concern nor the comprehension necessary to grapple with this problem of poverty in the fashion that the historical moment dictated. On the urgent issue of civil rights, Senator Goldwater represented a philosophy that was morally indefensible and socially suicidal. While not himself a racist, Mr. Goldwater articulated a philosophy which gave aid and comfort to the racist. His candidacy and philosophy would serve as an umbrella under which extremists of all stripes would stand. In the light of these facts and because of my love for America, I had no alternative but to urge every Negro and white person of goodwill to vote against Mr. Goldwater and to withdraw support from any Republican candidate that did not publicly disassociate himself from Senator Goldwater and his philosophy.
As his son says:
However, in a 2008 Associated Press story, King’s son and namesake Martin Luther King III said:"It is disingenuous to imply that my father was a Republican. He never endorsed any presidential candidate, and there is certainly no evidence that he ever even voted for a Republican. It is even more outrageous to suggest he would support the Republican Party of today, which has spent so much time and effort trying to suppress African American votes in Florida and many other states."
Next time a republican tries to tell you that MLK Jr. was a republican, or buys a billboard to announce it, now you know the rest of the story!