Can I use a 1/8 water supply line for a dryer with steam refresh option?
In the plumbing world this is fine.  However it might not be fine with your dryer.  You will need to read the manual or call the manufacturer to get an answer.  

I don't foresee a dryer using a steaming feature needing more than a 1/8" line but who knows if there is some sort of pressure rating needed.  It is probable that the manufacturer doesn't use 1/8" because it just isn't a commonly used size anymore and you can get screw hoses from big box for larger sizes.