I don't think switching those verbs is a good idea, Shirley Ling. I'd say that he "called time" or "called a time-out". "Taking time" doesn't sound idiomatic in that situation, and people might not understand what you were trying to say.
In football, each team has a limited number of timeouts they can use in a game. So we can say that a quarterback "took" (used) one of those timeouts. Baseball has no such limits, so we just say the player "called" time. (Technically, the umpire calls time; the player can only request time. But this is universally ignored by people who aren't umpires .)
To "take time" is a phrase in its own right that means to consume or spend an amount of time on something.
The game took a lot of time: the game lasted longer than usual. Take your time: Use or spend as much time as you need.
I think that literally one should write, "The catcher called, 'time.'" The catcher (or any other player) requests a suspension of play by saying the word "time" to an umpire. As pob14 points out, it's an umpire who stops play. If he doesn't, then the game continues. A runner on base may advance to the next base, for instance. I think there are other games in which a player may ask officials to suspend play by "calling time," such as tennis. There might even be games in which a player can temporarily interrupt the flow of play by "calling time" himself.
"Taking" time and "calling" time are not closely related, and certainly are not synonyms.