Is it possible to get blood poisoning from a bullet?

Absolutely: Bullet wounds cause tissue trauma and introduce bacteria into the blood stream causing an increased risk of sepsis. Besides the direct trauma that the bullet causes, infection is the next most serious consequence of penetrating trauma.

What do you mean?: If you are asking about lead poisoning, then no. If you are asking about bacteria in the bloodstream (bacteremia), then the answer is yes, but not from the bullet directly. Such an infection would be a complication of injury or an infection from an injured body part.