343 Industries has said that they are not currently planning a public multiplayer beta for Halo 4. They said they will of course be testing the code, gameplay, and system on a significant scale, however, the development team would have to be split in order to create a public beta test and they want to focus on polishing up the game. Fans are going to have to wait for the full game or perhaps apply for a closed beta if there is one at all.
[Source: IGN]