Rodri told broadcasters ^^^the referee has to be neutral^^^ in a post-match interview after the draw at Tottenham
The 29-year-old was left angry by a Dominic Solanke goal being allowed to stand after the Spurs forward appeared to kick through the leg of the City defender Marc Guehi.
While the FA did not specify the exact comments the charge relates to, Rodri accused referee Robert Jones of not being "neutral".
"I know we won too much and the people don't want us to win, but the referee has to be neutral," said the Spain international after the game.
"It's not fair because we work so hard. When everything is finished, you are frustrated."
Rodri is accused of acting in an "improper manner" by making comments that "imply bias and/or question the integrity of a match official".
He has until 18 February to respond to the charge.
City had led 2-0 at half-time at the Tottenham Hotspur Stadium on 1 February and looked set to clinch three points until Solanke's controversial 53rd-minute strike gave the home side hope.
He then pulled Spurs level with 20 minutes left.
In his post-match interview, Rodri said Solanke's first goal had potentially been a turning point in the outcome of the match.
"It's the first goal they score, maybe [if] they don't score this goal we win the game," he said.
He then alleged City had regularly fallen victim to poor decisions by officials in this campaign, where they are currently second in the Premier League table, four points behind Arsenal.
"It's one game and another game and another game - and it's not possible," added Rodri.
"Honestly, I never speak about referees, I respect their job massively. But they have to pay attention to these things.
"He (Solanke) kicked the leg, it's so clear... It's two, three games in a row and I don't know why."
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