There is no built-in command that does what you want.
One way to do something like it "manually" is:
<C-c>ciw
<C-c> to leave insert mode without triggering autocommands, leaving the cursor on the last <Space>,
ciw to cut the sequence of <Spaces>, which Vim treats as a "word", and enter insert mode.
Now that we have a working macro, it is trivial to map to something convenient:
inoremap <key> <C-c>ciw
And we can make it even better by preventing it from polluting registers with useless s:
inoremap <key> <C-c>"_ciw
Note that this mapping works for any sequence of <Tab>s and/or <Space>s as well.
Now, as noted by @Eineki, the mapping above is not a true inverse <C-i> because it deletes all the contiguous whitespace before the cursor, regardless of tabulations.
If you only pressed <C-i> once, then that mappings will effectively act as an inverse <C-i>, but if you have more than a &shiftwidth of <Space>s, the whole sequence will be deleted, which is not what a true inverse <C-i> would do.
A true inverse <C-i> would delete <Space>s up to the previous tabulation, which sounds a tad less trivial.