Removing rust stains from silk, particularly silk clothing, can be a real challenge. There are, however, a few things you can try. Whichever method you choose, you'll want to try the method on an inside seam or other hidden place on your silk item before you try it in a visible area, just in case your silk has an adverse reaction to any of the methods.
The first option you can consider for removing rust stains from your silk (besides the most recommended one, which is to take it to a professional cleaner right away) is to put salt on the stain and squeeze lemon juice over it. Then you have two choices: you can rinse it out right away or place it in the sun and leave it there for awhile.
Some people suggest using Bar Keeper's Friend cleaner and polish, but I admit that I am wary of it, possibly because I do not think the idea of using any kind of "polish" on silk sounds completely sensible. I mention it, though, in the interest of making this a complete set of tips. According to the official website, all you need to do is make a paste of Bar Keeper's Friend with water and apply it to the stain. If your garment is yellowed from rust in water, you will need to soak the silk in a bucket filled with a well-dissolved solution of water with one and a half cup of Bar Keeper's Friend. Again, test these methods somewhere inconspicuous first, just to be sure of your results.
There's also the option of going for the big guns and using a rust remover (such as RoVer or Whink), washing, then (if the stain has not been removed) using a spot treater (like Shout or some other pretreatment spray), washing, then (if the stain STILL has not been removed) using an all-fabric bleach, which should be safe for colored fabric.
You may also wish to consider trying oxalic acid crystals dissolved in water, but it might not be possible to find the crystals easily at the stores in your area. One last idea is to try some hydrogen peroxide, but do not leave it on any dyed silk too long or you will have a white spot.