Silk CAN be ironed.
More Info: Silk is a delicate fabric and must be ironed with caution. Many who own silk garments find that a small hand steamer is easier to use than an iron.
How to Iron Silk
Silk will iron more readily when slightly damp. If you have hand-washed your silk garment, roll it in a towel to absorb the moisture and let sit for half-an-hour. When you are ready to iron, turn the garment inside out to iron on the wrong side.
Using a moderate setting, place the garment, now turned inside out, on a cloth-covered ironing board. (If the iron has a specific heat setting for silk, use that.) Place a press cloth or linen towel over the silk garment before you begin to iron.
Use steady motions as you move the heat over the press cloth with the silk garment beneath it. Do not allow the iron to pause in one spot.
“Hints for Freshening Out Millenary Materials of All Descriptions.” University of Wisconsin. N.p., n.d. Web. 11 Jan. 2012. <images.library.wisc.edu/HumanEcol/EFacs/MillineryBooks/MBBottomleyGuide/reference/humanecol.mbbottomleyguide.i0005.pdf>
Heloise. “Hints from Heloise.” Gettysburg Times 28 Oct. 1986, Evening ed., sec. Our Times: 6. Print.