Ants DO have muscles.
Like all insects, ants have three body segments--the head, the thorax, and the abdomen. Depending on the species, the ant's abdomen is further segmented into sub-sections in the following order in relation to the thorax: the propodeum, metasoma (which in some ant species is also segmented into the node and petiole), and the gaster.
What Is a Muscle?
By definition, a muscle is an organ by which contraction produces movement. Muscles can be subdivided into extrinsic and intrinsic muscle groups. Intrinsic muscles are those that are fully contained within an area including origination, the innermost portion, and the point of attachment at the end of the muscle. Extrinsic muscles do not originate in the limb where the end of the muscle is attached.
Ant muscles are located in the metosoma and function to power the three sets of articulated legs. There are seven segments in one hind leg alone including the coxa, trochanter, femur, tibia, tarsus, pre-tarsus, and the tarsal claw.
Ant's muscles are both extrinsic and intrinsic. Most of the extrinsic muscles work to move the coxa, which is the leg segment that forms the joint between the leg and the thorax. The intrinsic muscles are paired and work to move the legs in relation to one another. The extrinsic and intrinsic muscles work in tandem to propel the ant forward and support the body weight.