Though there is a very similar verse in Bhagavad Gita, there is no reference of Atmaa in that. Probably the translation of Prabhupada (ISKCON), which is quite famous, could be source of that slight error.
BG 2.22 - As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones.
Most of the people translate "soul = Atmaa". And this could be the reason of such misconception.
There is NO reference of "soul" in the actual Bhagavad Gita translations
Here is the more accurate translation from Gambhirananda:
BG 2.22 - As after rejecting worn out clothes a man takes up other new ones, likewise after rejecting worn out bodies the 'embodied one' unites with other new ones.
In the original verse, the word is Dehi (देही) and Not Atma.
This could also be the reason, why people in popular culture (such as movies), refer the term as "My soul (Atma) and your soul (Atma) are one" etc..