The Digital Signature Algorithm (DSA) is not recommended. While it is technically not broken, it suffers from two major issues that make it a risky choice.
For a long time DSA was only standardized for keys with a maximum size of 1024 bit. This is believed to be breakable by a powerful adversary. While larger DSA keys with a size of 2048 bit are possible, they are often not supported.
Another issue with DSA keys is that each key comes with a set of parameters. These parameters need to fulfil certain mathematical properties and there is no specified way how an implementation can check whether these parameters are good. There is no supported way to have known good and standardized parameters. Using malformed parameters can lead to surprising and unspecified behavior.
Due to these issues we recommend avoiding the DSA algorithm.
For more Info see Cryptography Dispatches: DSA Is Past Its Prime.