David Beckham -- 12-Year-Old Son Trains with Arsenal ... Dad Goes Crazy

David Beckham could have TWO future stars in his family -- because his 12-year-old son Romeo got a shot with Arsenal's youth team ... and Thursday he scored a goal in a match!

Beckham went crazy on the sidelines ... as Romeo scored the second goal in a 3-2 victory over Liverpool.

Beckham's older son, Brooklyn, has been crushing it with the Arsenal training squad as well -- the 15-year-old was recently called up to the Under-18 squad ... and experts say he's got real potential.