I'm assuming you mean other users photos (Leanna is right about your own)...the only way I've seen it work on an iPhone is to open the Instagram photo in Safari--then tap and hold to bring up the Save Image button. You cannot do it from within the Instagram app.
And to actually do that isn't very easy--the only way I could copy the actual image location from within Instagram was to do this:
-go to the image
-scroll down to the bar with 3 dots, tap it for Options
-when your Twitter compose box opens, select and copy the URL for the photo
-cancel the Tweet and open Safari
-enter the URL, go to the site, and tap/hold on the image to bring up the Save option.
You can save a bunch of steps if you're finding the Instagram link on Twitter in the first place: just hold the link, choose Open in Safari, then tap/hold the image.