Pennsylvania Governor Josh Shapiro shot his shot with LeBron James when the NBA star was a free agent ... and while he's not taking credit for bringing the King to Philadelphia, he's still pretty starstruck over their encounter.

Jacob caught up with Shapiro on the campaign trail Monday in Pennsylvania ... and the governor told us he personally pitched LeBron on joining the 76ers, selling him on Philly and its opportunities for philanthropy.

But Shapiro got the real surprise when LeBron recognized him ... recalling how the NBA superstar told him, "Thanks, Gov. I appreciate your work."

"LeBron knows who I am," Shapiro gushed ... though he insisted Tyrese Maxey, Jaylen Brown and the rest of the Sixers players deserve the credit for convincing LBJ to sign a two-year contract.

The conversation then turned to Haley Stevens' stunning decision to back Republican Mike Rogers over Democrat Abdul El-Sayed in the Michigan senate race ... and Shapiro wasn't exactly jumping to defend her.

He wouldn't directly criticize Stevens but made it known he's supporting Democrats across the board ... adding there's no room for antisemitism, Islamophobia, or any other form of hate in politics.

And with Election Day looming, Shapiro told us he's not taking his own reelection for granted, even with strong polling ... saying he's hitting 40 counties in 10 days to win over voters.

He declared ... "I don't mail it in. I compete for every vote."

Hey ... he already knows a thing or two about making a winning pitch.