Google+, the social networking site which was launched last July, is still not complete as there are no third party apps or tools to manage your account like Twitter and Facebook. Even though the API was made available by Google, it is not fully available to develop apps. You can cross post your Tweets to Facebook from Twitter, but no such service exists for Google+. We had covered few Google Chrome extensions like Publish sync, which does the job.
TwooglePlus is a new web app which can post your Twitter updates to Google+. TwooglePlus watches your Twitter account 24 hours a day and cross-posts your Tweets to your Google Plus circles. Its an online service, so no browser extensions or plugins to install.
You need to add both your Twitter account as well as Google+ account to the service and it monitors your Tweets and post them to Google+. TwooglePlus optionally unshortens links in your Tweets and you can cross-post from more than one Twitter account.
There are quite a few options available including selecting the circles and temporarily pausing the updates etc.
Note: One of main drawbacks of the site is that it asks for your Google username and password instead of oAuth. The developer has in fact explained the reason for such a move. Google+ API is read only, so you can only fetch the updates and not post updates, so in order to cross post, the service actually needs your user credentials. He also mentions that once the new API is made available, the service will be updated to oAuth. So it is up to the users to decide whether you want to provide the user credentials to a third party service.
You can also connect with the developer on Google+.