My son made $1600 last year, but rec'd a 1099. Do I have to file for him?

Yes.  Income reported in Box 7 of a 1099-MISC is considered self-employment income.  The filing threshold for self-employed income is net $400.  So your son must file his own return.  Be sure he indicates on his return that someone else can claim him as a dependent.

Thanks.  Can I file for him or does he have to file on his own?

You can't put his income on your return.  He must file his own separate return.