Is Amoeba an anaerobe?

No. Amoeba carries out aerobic respiration.

Amoeba depends on the diffusion of gases for breathing. As Amoeba lives in water, the dissolved oxygen from water diffuses into the body of amoeba through its thin cell membrane. The oxygen moves quickly into the whole body and is used for respiration inside the Amoeba cell. Carbon dioxide is given out as a result of respiration which diffuses out through its cell membrane into the surrounding water.