Google publicly stated that they do in fact use what they call Social Signals to help determine a websites ranking in Google in December 2010

... remember this is "old information", 6 months is an eon in "internet marketing time"

Real Time Search
Google has played with real time search results and has had a love/hate relationship with it.
GOOG needs to have real time search but there is no effective method of preventing "black hat" spamming methods from skewing search results.  The 2009 Iranian election protests brought twitter to the forefront of news delivery. In the time that has passed since then Google and Twitter have parted company in incorporating real time search in current search results.

So the real time search button has disappeared, does that now mean Twitter is not worth investing your time in?

Yes and No
Local SEO and wanting Google to trust your domain

Just because real time search pops in and pops out of current G results doesn't mean twitter and other social networks can't boost your domain's trustworthiness

Google assigns a trust factor to your domain... we purport our websites to be about our genre, Google assigns an internal score to determine which domains are trustworthy.

If you do business in one county and everytime you drive from one end of that county to the other end of it... and you "check in" using a smartphone: You have established in the algorithm's eyes that you do, in fact, have "something" to do with that county

... on the other hand, if you operate a "get moving quotes" type website, meaning your offices are in one state but you want to rank in the other 48 states, Google knows you haven't even visited those states, let alone "do business" in those states.. well Twitter isn't going to help you with that one.

Attempting to curry Google's favor on a national scale VS a local scale
Local is a LOT easier...

GeoLocation Social Sites such as Foursqure, Twitter, Identi.ca and Facebook Places all incorporate a post twitter feature all serve to establish, in the algorithm's eyes that you do in fact do business in the geographical area you purport to do business in.

So in answer to the question: Does Twitter Improve Your Ranking?

Ranking a company website Nationally? perhaps a lot less than it did before

In local SEO my battle testing is showing me that it does help.