McGlinchy was drafted by the Atlanta Braves in the fifth round of the 1995 Major League Baseball draft from Malden High School in Malden, Massachusetts.
Despite never having previously pitched above Double-A, McGlinchy made the Major League roster in 1999 after impressing pitching coach Leo Mazzone with his composure in spring training. In the 1999 National League Championship Series, he gave up the famous Grand Slam Single to Robin Ventura. He later appeared in the 1999 World Series, pitching two scoreless innings in relief of Russ Springer at Yankee Stadium.
McGlinchy was on the Opening Day roster to start the 2000 season but was placed on the disabled list in April. McGlinchy was activated from the disabled list on May 14 after a rehabilitative assignment but returned to the disabled list on May 25. He returned from the disabled list in the first week of September. He appeared in what would be his final MLB game on September 28, 2000.

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