If there ever was a candidate who is a natural as a Republican, it is Arthur A. Fletcher, who is showing spunk and flair in his race for mayor of the District of Columbia.

Fletcher's philosophy should warm Republican hearts. He believes in reliance on the private sector, traditional family values, the notion that blacks shouldn't be beholden to one party (Democrats), self-disciplined and plenty of competition in this vale of tears.

In a sense, Fletcher is a black "Rocky" up against the celebrated champion, in this case, Marion Barry, the Democrat whose party has an incredible 10-to-1 edge in voter registration.

Just as Apollo Creed was supposed to flatten the unranked palooka challenger, Rocky, so Barry was to devastate any sacrificial lamb the GOP offered. But Fletcher, 53, is far more lion than lamb. He loves a fight, and like Rocky, is battling Barry for the full 15 rounds.

"The issues is which man is more comptent to run this city," Fletcher proclaims with gusto. "Black Democrats are asking who can better managed this government and be a credit to this city. Republicans, if they even ran, were always shut out from appearing before audiences. But I have been invited to traditional Democratic audiences and am getting some endorsements.

"I went table-to-table at the Black Caucus dinner - an all-Democratic affair - and got plenty of encouragement and some cash and donation pledges besides. Some black Democrats up against monolithic machines said it helps them that a Republican like me would take on the powerhouse here.

"Even when I first went before the D.C. Republican Committee their attitude was such that I didn't know if I was enemy or friend. I didn't expect them to see me as 'Bubblin' Brown Sugar' himself. I had to really talk to get them out of their private-club mode and defeatism. I've got them up to the 50-yard line now."

Fletcher's last public job was deputy assistant to President Ford for urban affairs. Earlier, he was alternate-delegate to the United Nations and for two and a half years was an assistant secretary of labor in the Nixon administration. He was once assistant to Washington Gov. Daniel J. Evans, and when he ran for lieutenant governor in that state, got 48 percent of the vote. Once upon a time Fletcher, a big rangy man, played football for the Los Angeles Rams and the Baltimore Colts.

Barry, 42, is yesterday's radical, now adopted by what passes for radical chic in Washington. His headquarters are heavy with accents from the Ivy and Junior Leagues. His deportment as civil-rights activist, school-board president, City Council member - in or out of fashionable dashiki - once caused frightened souls in the white power establishment to see him as a sort of Stokely Carmichael. His backers argue, however, that Barry has matured, has years of experience in D.C. problems, unlike Fletcher, who has never been directly involved in local government here.

Some black men of the cloth are still skeptical. "A soundrel is still a scoundrel," one minister preached here recently. "The same police that are backing him [Barry] were locking him up weekly. The same Board of Trade that gives him all the money was asking police to lock him up. The same ministers now inviting him to their churches then asked him not to come."

Even today, some clergy are unhappy with Barry's support of rights for gays, a referendum on legalized gambling, and easing the already eased penalties on marijuana in D.C. Consequently, the Council of 100 Ministers (who are black) endorsed a Republican Fletcher, for the first time.

Fletcher sees this as a sign that "family values are beginning to dominate the thinking in the black community." He thumps hard against crime and lectures that juveniles "must be told and shown that it takes fewer brains and even less guts to sniff 'coke' and 'shoot up' then it does to maintain self-discipline and self-respect and become self-reliant despite obstacles. They must be told and shown the benefits of listening to parents and teachers as much as radio disc jockeys and pop singers."

That is an obvious appeal to bourgeois values, but Fletcher couldn't win the support of middle-class and rich businessmen. Not only did the prosperous merchants, realtors, bankers and executive belonging to the Board of Trade flock to Barry's fund-raising luncheon; some brought envelopes stuffed with money and checks as well. The take for Barry: $60,000. Barry's total reported campaign expenditures this year: $364,379, Fletcher's: $33,288.

"Barry used to holler, 'Burn, baby, burn,' and threatened the same businessmen who now run to him," Fletcher says, laughing. "They are supposed to be hard-nosed, bottom-lined guys. How can they go for someone who mismanaged Pride (the black self-help program), whose enterprises went broke, and let him run a billion-dollar corporation like the District of Columbia?"

Fletcher must know the businessmen's cynicism is the same kind he experienced when he was a star high-school athlete back in Kansas and hosts schools asked him to go down alleys to eat in kitchens, or the segregation he lived with a truck driver in the "Red Ball Express" outfit which helped Gen. George Patton rush into the Battle of the Bulge in World War II. Fletcher was later wounded in the chest in the push through Germany.

The last GOP candidate for mayor here got 3.5 percent of the vote, and few can remember his name. Fletcher will be remembered. Barry, like Apollo Creed, won't forget this encounter.