Yes pigeons do carry disease that can be transmitted to humans.
One disease and condition that a pigeon carries and can transmit to humans is E. coli.
The E Coli can be transmitted to humans from the pigeon poop when the pigeons poop or droppings land and end up in a water or food supply and are then consumed by humans.
Sometimes you may not know that you consumed food or water that had pigeon dropping in it and then later you may contract E Coli.
That's why it's important to keep pigeons away from food sources and water sources where humans will be consuming it.
You can also get a few other diseases from pigeons which are Histoplasmosis and Candidiasis.
The Histoplasmosis is a respiratory disease that can sometimes be fatal and the Candidiasis is a yeast infection is spread from pigeons to humans.