I know that iCloud currently supports only syncing your Safari bookmarks with Safari on Mac or PC and IE on PC. However I'm using Chrome on both those platforms and I'm wondering if there's any workaround to have Chrome bookmarks synchronized with iOS devices
Well, as a workaround, you could use Xmarks.
Syncing your bookmarks with Xmarks works with both Chrome and Safari, so anything you add in Safari will appear in Chrome and visa versa.
That way you can also add a bookmark in Chrome, it will sync to Safari over Xmarks and then out to your iOS devices with iCloud.
Probably not what you wanted, but it will work. It's what I ended up doing.