You can definitely download it directly to your phone but you may need to try a different browser. For example Firefox. I use Firefox for all my downloads but not much as a browser.
I did this with my Nexus 7 without issues. The use a free app called Androzip from the playstore to unzip it. The official link for the Cleo download page is here:
http://www.dev-c.com/misc/cleo-android/
And the page is this with info is here:
http://gtaforums.com/topic/663125-android-iiivcsa-rel-cleo-android/
Hopefully this will help anyone else looking for Cleo.
By the way for anyone having trouble activating Cleo I find that if I hold my thumb at the bottom center of the screen and position my index finger close to the top and then slide it up farther the app activates without much effort.
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