No. A woman (at least a woman who was born a woman) doesn’t have a Y chromosome.
If you have one or more “Y” chromosomes, then you are a biological male.
* A normal male has an “XY” chromosome pair.
* A male with Klinefelter’s Syndrome has “XXY.”
* A male with Supermale Syndrome has “XYY.”
If you have no “Y” chromosomes, then you are a biological female.
* A normal female has an “XX” chromosome pair.
* A female with Turner’s Syndrome has one “X.”
* There are females known as XY-females, but these are really biological males who had suffered an “unfortunate” injury while in the womb or during birth and were raised as females.
There may be other combinations that I am not aware of, but it is the presence of a “Y” chromosome that makes you biological male, and the absence of a “Y” chromosome that makes you biological female.
Of course, you can be biologically male and be anatomically female through surgery, and visa-verse. But you can’t change what you are genetically.