Can I cut my micro sim to fit iphone 5s

It is not recommended. It would be better to get a nano sim from your carrier. If your carrier does not have nano-sims, you may want to change carriers to get a proper nano-sim.

http://www.redmondpie.com/how-to-convert-micro-sim-to-nano-sim-for-iphone-5/

call me Mr. Google-it

Why don't you just ask your carrier for the nano sim?