Can I apply for a patent for the idea of adding a camera to a mobile phone?

All technical solutions can be patented. I think your question is whether you can get a patent, or whether it meets the three characteristics of a patent.

The simple existing technology is patchwork and does not change their respective functional effects, which is arguably not creative. However, if the existing technology has a mobile phone and a camera, but it is difficult to implement, and your technical scheme effectively overcomes this difficulty, or your technical scheme can achieve unexpected technical effects, then this technical scheme is patented and may be authorized.

If there is relevant existing technology, the application for utility model should also be authorized, because utility model does not need to be audited. But such rights are meaningless and easy to fail.