In addition to being a way to collect and manage content, Inoreader.com also syndicates content, sending it back out in the form of RSS feeds that you create and configure with Inoreader folders and tags. So, for example, I use Inoreader to create a "combination feed" that shows my Twitter posts and my Google+ posts and my blog posts, all combined into a single feed which you can see at my homepage, MythFolklore.net. Here's a screenshot:
So, if you are interested in having a Twitter archive, consider giving Inoreader.com a try. And feel free to contact me with any questions you have about Inoreader; I'm one of their biggest fans!
NEXT STEP => With the next tool, you'll see another way to aggregate Twitter content, but this time it is based on collecting tweets for a specific hashtag: Tagboard.