Does your photo on Twitter go on google images ?

[Tina Smith]

And if it does are there privacy settings so they won't go on

[DR Tech]

Yes, anything made public can be searched. No their is no particular setting to prevent it to be added on google images.

Their is a saying, if you don't want it public don't put it on the internet. What you can do is the file name you upload it as some random letters. As the image is searched first the file name then the user accoutn name. As long as these are not associated it will be harder to find. That is really as much as you can do if you still want to use the service.