Twitter.com does not natively return canonical profile URLs. That is, Twitter does not redirect any form of a Twitter URL that resolves successfully, nor does it employ the <link rel="canonical"> element on profile pages as a "hint" to the search engines.
However, Google does seemingly index different URL forms of profile pages separately – the most common being the non-trailing slash form (http://twitter.com/profilename), the trailing slash form (http://twitter.com/profilename/) and the secure form (https://twitter.com/profilename).
It also appears that the different forms of a profile URL are being accorded different PageRank based on inbound link metrics.
While neither the search engines nor Twitter seems to take profile URL case into account (both twitter.com/aaranged and twittercom/AaRaNgeD resolve succesfully and carry the same PageRank), the search engines do take case into account when returning twitter profile URLs in snippets. A search for "barack obama twitter" in Google returns the snippet URL "twitter.com/BARACKOBAMA" while same same search in Bing returns the snippet URL "twitter.com/BarackObama". Whether this is related to the first-spidered link, the most common form of a link, the authority of linking locations or other factors is uncertain (there are actually few "BARACKOBAMA" anchors in this profile's external link environment).
All things being equal, a page with a canonical URL should rank higher in the SERPs than that same page accessible under multiple URLs, chiefly because inbound link popularity is not split between different URLs returning the same content. So if it's important to you that a Twitter profile has maximum visibility in search results for a given keyword (most likely those related to brands and personal names), do what you can to help the search engines work out the "correct" version of your profile page. The takeaways here are pretty straightforward:
- In links, use the profile form of the URL without the trailing slash. While this is normally a "pick one and stick with it" decision, in the case of Twitter profiles the non-trailing slash form will be propogated whether you like it nor not, as databases that list Twitter profile URLs on spiderable pages tend to favor this form of the URL (e.g., wefollow).
- Consistently use this form of the profile URL in all links you encode – keeping in mind that this not only controls links directly under your control, but that the form of links on your own authority sites are those most likely to be copied and pasted.
- Don't link to a profile using https://.
- Consider the implications of adding tracking parameters in links to a Twitter profile, and avoid doing so if there's some other way of you tracking clicks on these links.
Perhaps Twitter will eventually do this work for you by canonicalizing profile URLs on their end (Facebook redirects the trailing slash form of pages to their non-trailing slash form, and https:// requests to http://) – I certainly urge them to do so.