The students are among the victims in more than a dozen states who were targeted.
The messages come from unknown numbers.
They tell people they've been selected to "pick cotton at the nearest plantation."
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Some of the texts reportedly mentioned the incoming presidential administration.
Louisiana Attorney General Liz Murrill says her cyber team discovered the messages can be traced back to an anonymous web address in Poland.
"FBI says it is investigating they'd like to determine whether this is a foreign source that these who are some kind of domestic source, whether it's a prank or something more sinister," according to ABC News reporter Aaron Katersky.
Some of the messages were sent from a free calling and texting app.
The app says those accounts were quickly disabled and it is cooperating with law enforcement.
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In a statement, San Francisco Unified says hate will not be tolerated and it's providing wellness support to any student who has been affected.
The district says it will cooperate with any law enforcement investigation into the messages.
"We're going go turn within and make sure we take care of our children and that we keep our communities safe from this uncivilized behavior," said Rev. Amos Brown.
San Francisco Mayor-elect Daniel Lurie put out a statement on "X," saying he's spoken with Reverend Brown.
He also said he stands with community leaders in condemning the messages.
The NAACP is also holding a town hall on the issue on Sunday.