Rodent that is around makes you angry (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'rodent that is around' is the wordplay.
'rodent' becomes 'rat' (rat is a kind of rodent).
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'around' indicates putting letters inside.
'rat' going within 'ie' is 'IRATE'.
'makes you' is the link.
(Other definitions for irate that I've seen before include "Annoyed, irritated" , "Not happy" , "Ticked off" , "Narked" , "Angry and incensed" .)