Very likely. But it is common enough all around the primitive world that it is not impossible they already had it.
Here is reasonable argument (not proof) against Jews getting it from the Egyptians, quoting the Bible without necessarily literally believing the historicity of the story.
First the quote: Exodus 4:24-26 King James Version (KJV)
The interpretation:24 And it came to pass by the way in the inn, that the Lord met him, and sought to kill him.
25 Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast it at his feet, and said, Surely a bloody husband art thou to me.
26 So he let him go: then she said, A bloody husband thou art, because of the circumcision.
Egyptians practiced circumcision as a puberty rite of passage (as is most common), Jews on eight day old infants.
Moses, being an Egyptian prince by upbringing (never mind his non-historicity) was waiting when it came to his own kids.
And God was angry about that.
His wife saved the day.
Check with Doctor X about when that was really written, etc.
Jews do it different from the Egyptians, therefore got it independently.
Relevance to modern day Judaism:
Women are allowed to perform circumcision when no man is around who will do so.
A Jewish historian I know (not religious and not professionally concerned with Biblical era stuff), once opined that circumcision is "obvious".