As long as the food is frozen completely and you have the frozen food packed with ice or ice packs that are completely frozen then yes you can bring frozen food on the plane in your carry on luggage as well as in your checked luggage.
The ice must be completely frozen or the ice packs must also be completely frozen before they'll allow it through the airport security.
If the ice is melted or the food is thawing out then the frozen food will not be allowed through the airport security or in your checked luggage or carry on luggage.