Like much of life, making your Shimano disc brakes work with your 160mm rotor is easy --once you learn how to figure out which adapter you need. Whatever you have, we can either sell you the adapters to make it work, or tell you that what you have is enough.
You need to know three things -- what kind of mount your Shimano disc caliper is, International Standard (ISO) or post mount. If it goes on the front, you need to know what your fork is: ISO, post-mount, or a few special cases (Marzocchi 20mm axle, Boxxer-type). And, you need to know the rotor size that you're trying to fit -- in this case, it's 160mm.
If you're trying to diagnose what you already have and/or what you need, here's how to do it. The Shimano adapters all have a model number that starts with SM. The Mount Adapter acronym is MA. Front brake is F. Rear brake is R. Rotor Size is 140, 160, 180, or 203. Caliper Mount Type will be S for ISO/International A, and P will represent Post. And the last letter will be for the frame or fork mount type: S for ISO/A, P for Post, B for Boxxer, Z for Marzocchi 20mm Axle as well as QR20Plus and DH ISO. Thus an adapter that reads SM-MA-F-203S/P is Shimano Small Parts Mount Adapter Front 203mm Rotor with ISO caliper on a Post type fork.
With the first drop down box, please select the mount that corresponds with the fork or frame you are using. With the second drop down box, please select the type of caliper you have -- Post or International Standard (ISO).