Stain Removal Tip for Rust:

Saturate the spot with lemon juice, using a spray bottle, and allow to remain for 5 minutes.

To remove the lemon juice, apply a small quantity of detergent solution to the spot. Use a blotting motion to work the detergent into the affected area. If the spot is being removed, continue applying detergent and blotting with a white paper towel until spot is completely removed. Rinse with tap water using a spray bottle and blot to remove excess moisture. Then spray lightly with water, but instead of blotting, apply a pad of paper towels and brick and allow to dry. If there is still some stain on the carpet and blotting is not removing it, moisten the tufts in the stained area with 3% hydrogen peroxide. Let stand for one (1) hour. Blot and repeat until carpet is stain free. Light will cause peroxide to change back to water, so no rinsing is necessary. Apply a pad of paper towels and weigh them down with a brick.

If this does not work, call a professional. Note: Most rust removers contain a very strong acid and are therefore not recommended for use by homeowners.

REMEMBER! Never use a circular motion to remove a spot as this may destroy the texture in the spot area.

Source: Wear-Dated Carpet Spot Cleaning Guide