Some agricultural professions have specific names assigned to them. For example, a person who raises sheep is a shepherd and a person who raises cattle is a rancher. What would a person who raises turkey (or perhaps poultry in general) be called?
Poult (The American Livestock Breeds Conservancy)
"is a young domestic (not wild) turkey."
"Poultry are domesticated birds that are kept for meat or eggs including birds of the order Galliformes: chicken, turkey, natatorial (swimming) birds: duck and goose."
If you want to be technically specific, it would be poulter.
Informally, you can say turkey farmer.
mid-14c., from O.Fr. pouletrie "domestic fowl" (late 13c.), from poulet "young fowl" (see pullet). Poulterer (1630s) is a redundancy, but has largely ousted original poulter (c.1400), from O.Fr. pouletier "poulterer," with agent suffix -er. Poetic poulter's measure (1570s) is of fanciful origin.