The justices said they will review a lower-court ruling that found problems with two congressional districts and statehouse districts in four counties.
The lower court had ordered the districts redrawn in time for the 2018 elections, but the Supreme Court blocked those orders last year.
Primary elections are scheduled for March under the existing, challenged maps.
The court probably will hear arguments in April and decide the case by late June.
The dispute over the Texas maps focuses on racial discrimination and is separate from the high court's ongoing consideration of excessive partisanship in redistricting in Maryland and Wisconsin.
Texas' congressional and legislative districting plans have been embroiled in court action for years, beginning in 2011.
After the state's original maps were tossed out as unconstitutional, a three-judge federal court produced interim districting plans that were used in the 2012 elections.
In 2013, Republicans who control the state government rushed to permanently adopt those maps to use for the rest of the decade, until a new round of redistricting after the 2020 census.
But opponents criticized the adopted maps as a quick fix that didn't purge all districts of the impermissible use of race.
In 2017, the same judges who approved the interim maps in 2012 agreed with the challengers that the maps were the product of intentional discrimination.
Texas Attorney General Ken Paxton, a Republican, said in the state's appeal that the lower-court ruling is a "remarkable decision that defies law, logic and fact."
In urging the justices to ratify the decision by the three judges, civil rights groups said that almost all the districts at issue were originally adopted by Texas lawmakers in 2011 and were rife with racial bias.
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