Are there any STDs that can make your penis bleed?

Condyloma. A genital wart (condyloma) in the urethra can present by small amounts of blood found at the meatus or in the linning of your underwear. If the blood is in the urine or ejaculate, there are many possible conditions to consider.
Sure. Of course, one sign of several stds can be bloody penile discharge. Get tested asap or any time this happens.