While Texas Republicans, including Senator John Cornyn, have requested FBI assistance to locate and arrest Texas Democrats who fled the state, the FBI has indicated no plans to intervene, and the legal authority for federal arrest and forced return is highly questionable.
FBI can arrest Texas Democrats and have them come back to Texas

Texas senator asks FBI to help locate and arrest Democrats for leaving state - Texas | The Guardian
Source: theguardian.com
Key Evidence
Senator John Cornyn asked the FBI to help locate and arrest Democrats who fled Texas.
axios.comaxios.comTexas lawmaker asks FBI to help arrest fleeing Democrats
Governor Abbott ordered state troopers to arrest absent Democrats.
bbc.combbc.comTexas Republicans vote to arrest Democrats stalling redistricting vote
A Trump administration official confirmed no plans exist for federal agents to intervene.
forbes.comforbes.comTexas Senator Asks FBI To Arrest Democrats Who Left State Over Redistricting...
What the Evidence Shows
Texas Republicans, led by Senator John Cornyn and Governor Greg Abbott, have sought to compel Democratic lawmakers who left Texas to prevent a quorum by requesting law enforcement, including the FBI, to locate and arrest these lawmakers and bring them back to the state legislature.theguardian.comtheguardian.comTexas senator asks FBI to help locate and arrest Democrats for leaving state
axios.comaxios.comTexas lawmaker asks FBI to help arrest fleeing Democrats
thehill.comthehill.comCornyn presses FBI to help Texas bring back Democrats who left state
Governor Abbott has ordered Texas state troopers to arrest and return absent Democrats, and civil arrest warrants have been issued by the Texas House for these members.bbc.combbc.comTexas Republicans vote to arrest Democrats stalling redistricting vote
cnn.comcnn.comWhat happens next in Texas redistricting and for Democrats facing civil arrest...
However, an unnamed Trump administration official has publicly stated that there are no plans for federal agents such as the FBI to be used in this matter, emphasizing that state authorities can handle it.forbes.comforbes.comTexas Senator Asks FBI To Arrest Democrats Who Left State Over Redistricting...
The FBI’s jurisdiction is limited primarily to enforcing federal laws; arresting state legislators for absence or quorum issues is a state matter. The use of federal law enforcement to enforce state legislative attendance is unprecedented and legally dubious.
Therefore, while the claim that the FBI can arrest Texas Democrats and bring them back is based on requests made by some Texas Republicans, it overstates the FBI’s role and authority in this situation. The FBI has not agreed to participate in such arrests.
In summary, the claim conflates political requests with actual legal authority and federal law enforcement action. The situation remains a standoff primarily managed at the state level.