Currently, passwords are only synced in the desktop Chrome
Chrome for Android is finally picking up steam, at least on the development side. A new beta channel was launched earlier this month and Google has been busy pushing updates to the new Chrome 25 for Android.That's the same version that desktop users get and the nice thing about that is that Android users will be getting updates and new features just as soon as everyone else.
The second big benefit is that the desktop and mobile versions of Chrome will work more tightly together. One feature that should come in handy especially on mobile devices is password sync.
You can save passwords with the built-in manager in Chrome for Android, but you can't import your saved passwords from the desktop.
But Google is working on it, already, you can enable password sync in the newly introduced "flags" page, full of experimental features. Just search for "Sync keystore encryption" in chrome://flags and enable it.
You probably should wait for the feature to be properly supported though, unless you don't mind losing your sync data accidentally.