Miami acquired McKinnie on Monday from the Baltimore Ravens for a conditional late-round draft pick.
The 34-year-old McKinnie will likely compete for playing time with right tackle Tyson Clabo, who allowed two fourth-quarter sacks in Miami's loss Sunday to Buffalo and has given up seven sacks this season.
McKinnie, who is listed at 6-foot-8 and 352 pounds but might be bigger, started all four postseason games a year ago at left tackle for the Super Bowl champion Ravens.
He also started the first five games this season, then he was benched in favor of Eugene Monroe and has since been inactive for the first time in his career.
''I appreciate my time in Baltimore & winning a ring along the way,'' McKinnie tweeted. ''Now time to move on.''
Coincidentally, McKinnie's final game for the Ravens came when they beat Miami.
''He's a really good player,'' said Dolphins defensive end Olivier Vernon, who butted heads with McKinnie. ''He's a big guy. That's a lot of man right there. He held his point really good against us when we played them, so it'll be a great addition to the team.''
The Dolphins (3-3) haven't won in a month. In the past three games, they've allowed 12 sacks and committed seven turnovers - all by harried quarterback Ryan Tannehill.
The team's downward spiral threatens to gain momentum with the next two games against division leaders New England and Cincinnati.
''We're realistic in where we're at,'' receiver Brian Hartline said. ''We understand the drop-off we've had. But we're still alive; we're not a dead team.''
Poor pass protection for Tannehill has put playoff prospects in jeopardy, however. He leads the NFL with 26 sacks, and his fumble when sacked by Mario Williams in the closing minutes led to a Bills field goal that gave them a 23-21 victory.
Williams used a power rush on the play to beat Clabo, who took the blame.
The timing of the deal hints at the Dolphins' desperation for pass-blocking help. They haven't swung an in-season trade since Sept. 29, 2009, when they acquired quarterback Tyler Thigpen from Kansas City for a fifth-round draft pick.
Coach Joe Philbin resisted any temptation to shake up the offensive line when the team had a bye before the Buffalo loss. His day-after-the-game media session Monday took place before news of the trade surfaced.
''It's a good move for us, good move for Bryant,'' Ravens coach John Harbaugh said.
''He is a proven and experienced player who will be a great addition to the offensive line,'' Dolphins general manager Jeff Ireland said in a statement.
To make room on the roster for McKinnie, Miami waived linebacker Josh Kaddu.
McKinnie played for the Vikings in 2002-10 and made the Pro Bowl in 2009. Last season, he came off the bench for the Ravens during the regular season, then was a key figure in their run to the Super Bowl title.
But he missed the first day of training camp this summer for being overweight and struggled thereafter.
The trade means a homecoming of sorts for McKinnie, who won the Outland Trophy with the 2001 national champion Miami Hurricanes. Vernon also played for the Hurricanes, but said he didn't remember McKinnie as a collegian.
''Nah,'' Vernon said. ''That was when I was a little kid, man.''
AP Sports Writer David Ginsburg in Baltimore contributed to this report.
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