Have you tried moving the app itself to the SD card? Maybe it's not the photos, but the internal cache that's taking up all your storage.
Anyway, according to Instagram Help:
The Android app may take up more internal memory than other apps on your device because we cache photos, which makes the Instagram experience faster for you and conserves bandwidth (which means you don't have to re-download photos over your carrier's network). Note that as of v1.0.3, you can install the app on your device's SD card.
On Android, you can find out how much space Instagram takes up on your device by following these steps:
- Exit Instagram
- Open the Settings application on your device > Applications > Manage applications > Instagram
- Total Storage is listed on the Instagram screen.
If you choose Clear data, your download cache will be cleared. Clear cache will reset memory for the app.
There is not, otherwise, a way to tell Instagram to store your photos directly to your SD card.