I just listened to the Rolling Stone's 1965 version:
https://www.youtube.com/watch?v=gdFQtbXAWdc (First 20 seconds at 0.5 speed), and it's not a great comparison

That being said the Andrew Oldham 1966 cover version is a pretty strong match:
https://www.youtube.com/watch?v=9YrllfAMwHI
(I'd also say it's artistically better, with Futurama themes)

Edit:
Woah, okay I'm a fan of Andrew Oldham's Orchestra. They've done a few covers of Rolling Stones songs, and they all sound way waay better than the whiney steeley sound that I find grating about the Rolling Stones