Circa is used when a time or date would otherwise appear as definitive or precise if not marked in some way that it is not what is intended; and usually circa is relegated to referencing the past...and is generally abbreviated "ca." and appears preceding the time or date.
In the context, "the beginning of August" referencing a future event relative to today, it wouldn't be read as definitive or precise generally.
If a precise time is asked for and this is sufficiently "precise," then to establish this as merely an estimate where that window should not be held absolute, "circa" is the incorrect word. Instead, "approximately," or "tentatively" would convey the proper meaning:
"I'll finish my work, approximately, by the beginning of August."
Or
"I'll finish my work by the beginning of August, approximately."
Or
*"Tentatively, I have planned to finish my work by the beginning of August."
It all depends on context for word choice; professionally, the choice of "Tentatively" is probably appropriate, especially if you are addressing an Advisor or a Supervisor directly.
Formalities aside, and if someone is requesting that information that doesn't really need to know for any reason, then I defer to Donnie Brasco:
"...'eyyy...you know...forget about it..."