A private investigator that is an actual law enforcement officer or detective could indeed get a warrant and get your text messages from your cell phone provider.
However when it comes to just regular private investigators hired by just anyone then no those private investigators do not have any powers nor any of the powers to get a warrant to get text messages from your cell phone provider.
All a regular private investigator can do is to follow someone around legally and then observe their actions and what they are doing and where they are going.
Then the private investigator reports back to the person who hired them on what they've found out and provide pictures to them or videos of the persons actions and where they've been.
That's really all a private investigator can do for someone.
Although sometimes a private investigator may be summoned to show up to court in a court case if one is to happen to testify against someone.