Are some circular arguments reasonable? — forrest-sounds

Sure. Just not deductively (formally, syntactically, mechanically, automatically).

and is this an example of one? — forrest-sounds

So it depends on whether your circle is a tight loop, and has to have been spinning forever (unreasonable) or is more like a broth on a slow boil, added to and stirred, re-fried etc. (a culture).

This has nothing to do with circular arguments in the traditional sense. What you are asserting here is 'Sartrean' consciousness - the [self]-awareness of consciousness - as opposed to the simple, reactive consciousness of, eg, Behavioural Psychology,

I know I'm conscious,
because I am conscious.
Because I am conscious,
I know I'm conscious. — forrest-sounds

That only switches the order of the clauses 'I know I'm conscious' and 'because I'm conscious'.

That just redundancy, not circularity.