Swot up with American chap (6)
I believe the answer is:
marcus
'chap' is the definition.
'swot up with american' is the wordplay.
'swot' becomes 'cram' (synonyms).
'up' is a reversal indicator (in down clue: letters go upwards).
'with' says to put letters next to each other.
'american' becomes 'us' (abbreviation for United States).
'cram' backwards is 'marc'.
'marc'+'us'='MARCUS'
(Other definitions for marcus that I've seen before include "chap" , "boy" , "Man" .)