"pertaining to a tailor," 1807, from Modern Latin sartorius, from Late Latin sartor "tailor" (source also of French sartre "tailor"), literally "patcher, mender," from Latin sart-, past participle stem of sarcire "to patch, mend" (from PIE root *srko- "to make whole, make good"). The classical Latin word was sarcinator (fem. sarcinatrix).
Earlier in English in same sense was sartorian (1660s). Sartorius as the name of the long leg muscle (1704) is because it is used in crossing the legs to bring them into the position needed to sit like a tailor. Related: Sartorially.