Men without millions are inclined to sign up (6)
I believe the answer is:
enlist
'sign up' is the definition.
(enlisting is a kind of signing up)
'men without millions are inclined' is the wordplay.
'without' is a deletion indicator.
'millions' becomes 'm' (abbreviation).
'are inclined' becomes 'list' ('list' can mean to lean or tilt).
'men' with 'm' taken out is 'en'.
'en'+'list'='ENLIST'
'to' is the link.
(Other definitions for enlist that I've seen before include "Register" , "Sign on -- 13 (anag)" , "Enrol in armed forces" , "Join the military" , "Join up in silent way" .)