Born in Los Mochis, Mexico, Arce turned pro at the age of 16. He won his first four fights, then hit a snag against two future contenders. Arce lost to Omar Romero and drew with Gabriel Munoz in back-to-back fights in the summer of 1996, but then won 10 straight fights and a pair of regional belts before losing on points to veteran Jose Victor Burgos on December 12, 1997.
He recovered from that setback with four straight wins, earning his first world title shot on December 4, 1998 against Juan Domingo Cordoba for the WBO light-flyweight title. Arce won the fight and became a world champion at the age of 19.
After making one successful defense of his title, Arce drew a big-money fight in Tijuana against three-time former champion Michael Carbajal. Arce was ahead on all three judges' scorecards after 10 rounds, but in the 11th, the veteran Carbajal connected with a right hand and captured the crown via a technical knockout.
After a four-month layoff, Arce returned to the ring and won a WBO regional belt, while working his way back up the rankings for another title shot. That came on October 20, 2001, when he defeated Juanito Rubillar for the WBC version of the light flyweight title. He has held it ever since, making four successful defenses and winning two non-title bouts as of July 2003.
Towards the end of 2003, he participated in the Televisa version of Big Brother, the Big Brother V.I.P show that put celebrities together. He arrived in third place, then went training for his next defense, against former world champion Joma Gamboa on January 10 of the following year. He had planned to spend Christmas day back in Los Mochis with his family; however, because of the terrorism concerns caused by an Air France flight to Los Angeles, all airports in Mexico were closed that day. Arce then made a press conference, in which he said the memorable words: I missed being with my family on Christmas day, and I will have to miss being with them on New Year's eve. Because of that, someone inside the ring will pay!!.
Arce invited his Big Brother celebrity friends to the fight with Gamboa, his first fight of 2004, which he won by a second round knockout. But during and after the fight, chaos ensued: One of his friends, actress Arleth Gonzalez, was kicked off her chair by another person. And Veronica Castro was pursued by the press when she was trying to leave the fight site, taking her little more than two hours to get to the site's parking lot.
Arce's career record is 35 wins, three losses and one draw, with 26 knockouts. He is a perfect 14-0 since the loss to Carbajal.