That is the traditional belief, although the actual Luke 1:36 describes her as "relative", "syggenes".
Luke 1:36 And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren.
suggenes {soong-ghen-ace'}
Part of Speech:
adjective
Usage in the Bible:
kinsman 7, cousin 2, kinsfolk 2, kin 1