Not exactly. They may look similar, but there are significant differences.
First, the shape of the sari fabric is rectangular, while the shape of the toga fabric was more or less semi-circular. (It took a lot of effort and experimentation for a researcher to figure that out some decades ago, because the ancient sources do not tell us.)
In addition, a sari can be draped in several different ways, depending on the look you want, whereas there was only one really correct way to drape a toga. The main differences between togas involved colors (mostly variations on white) and borders. Sari fabric can be pinned in place, over a blouse and petticoat, but the toga was simply supposed to be draped over a tunic. However, given the annoyances of having to wear a toga, I wouldn't be surprised if some men occasionally used pins to help hold them in place. They were certainly used in other ancient garments.
Finally, of course, the sari is a garment for women, while the toga was for men. Roman women wore a garment called a "stola" over a long dress.
The sites below are instructive:
https://www.singhanias.in/blogs/singhanias-saree-journal/how-to-wear-a-saree-step-by-step-guide-to-draping-a-saree-perfectly?srsltid=AfmBOorORapQK1uAo78qjy0Qm1bpGxqIz4RcAodgKp76YJZnt2b4u2dH
https://www.tastesofhistory.co.uk/post/the-toga
