Something that could be used with Tweetbot would be great! I'm not particularly happy with any of the options I'm aware of (imgur is not one of them).

I've attached their spec for quick reference:

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HTTP POST which includes the Twitter OAuth Echo headers (described http://dev.twitter.com/pages/oauth_echo)

POST includes the following fields:

    - message: text of the tweet
    - source: "Tweetbot for iPhone"
    - media: JPEG or MP4 data with a mime type of image/jpeg or video/mp4 and a file name of either image.jpg or movie.mp4

response should be in one of the following formats:

    - <mediaurl>URL</mediaurl>
    - { url: URL }
    - { mediaurl: URL }

Their cited example: https://mlkshk.com/upload