You can have your MU flights credited to Asia Miles. You can redeem Asia Miles on a number of carriers including AA, AS, and BA. This is probably the best option unless you plan on flying MU a lot.

www.asiamiles.com

If you anticipate flying MU frequently, then you can join their own program which used to be called Golden Swallow but is now Eastern Miles. I think you used to be able to enroll online at www.ce-air.com but the new www.easternmiles.com site appears to only be in Chinese. Since this change, I haven't been able to make heads or tails of how many kilometers are in my account.