Earthworms belong to the Phylum Annelida and particularly the genus Lumbricus. The Phylum is characterised by body segmentation and a body cavity called acoelom. It includes marine worms, leaches and earthworms. The Earthworm belongs to the Phylum, Annelida Earthworms belong to the Annelida phylum.
Earthworms belong are Annelids which belong to the Kingdom Animalia so technically they are animals. Insects are also animals (Animalia). But no, earthworms are not insects.