Laugh about wag's first tweet (7)
I believe the answer is:
'tweet' is the definition.
(I know that tweet can be written as twitter)
'laugh about wag's first' is the wordplay.
'laugh' becomes 'titter' (titter is a kind of laugh).
'about' indicates putting letters inside.
'wag's first' becomes 'w' (1st letter of 'wag').
'titter' going around 'w' is 'TWITTER'.
(Other definitions for twitter that I've seen before include "Chirping (could be electronic!)" , "Latest craze in web-based messaging" , "Chirp; trivial gabble" , "Bird's sound; trivial talk" , "Social networking site" .)