Rondon, a 2012 international free-agent acquisition, was 1-1 with an 8.64 ERA in two starts this season for the Angels' rookie-league affiliate in Arizona.
The Angels sent $879,500 in pool money to the Rangers on Thursday for right-handed pitcher Jason Hoppe, and $239,400 to the Mets for righty Gaither Bumgardner.
Last year, the Angels forfeited the right to spend more than $300,000 on any prospect for the following two international signing periods when they acquired Cuban shortstop Roberto Baldoquin with an $8 million signing bonus.
The Angels entered the international signing period with a bonus pool of $1,968,600 -- the lowest in baseball, because the team finished with a Major League-best 98 wins last season.