Is there a rule to this in baseball?

With a runner on first only, the fielder can let the ball fall untouched. But if he gloves it and then let's the ball drop, the batter is out, and the runner is not forced.

And no, this is not an infield fly situation. For that, you need runners on first and second, or bases loaded.

Here's the rule with one runner on first:

6.05(l) The batter is out when an infielder intentionally drops a fair fly ball or line drive, with first, first and second, first and third, or first, second and third base occupied before two are out. The ball is dead and runner or runners shall return to their original base or bases. APPROVED RULING: In this situation, the batter is not out if the infielder permits the ball to drop untouched to the ground, except when the Infield Fly rule applies.

If the fielder allows the ball to fall untouched and it becomes a fair ball, this is legal.

If the fielder manipulates the ball to the ground (like lettting hit in the glove and fall straight out) the ball is dead, the batter declared out and all runners returned to base occupied at the time of the pitch. This is called an intentionally dropped ball and it is illegal for an infielder to do so.

Not with a player only on first base, no.

If there were runners on first and second or the bases were loaded with less than 2 outs, it would be called an "infield fly", meaning the hitter is automatically out (regardless of whether or not it was caught) and the runners could advance at their own risk (still following the rules of tagging up if the ball is caught)

The reason it does not apply with only a runner on first is fairly simple - chances are the hitter would be able to beat out a pop-up if they chose to go to second first, making it very difficult to turn the double play anyway.

yes its called the infield fly rule