Upvote:1
We actually can't know whether you need a visa to enter the UK without knowing your nationality, the nature of your residence permit, and whether you will be traveling with your wife to the UK (or joining her there). The rest of this answer assumes that people with your nationality normally require visas.
We can say that your status in Germany only allows you to travel to the UK if your residence permit is a "residence card for a family member of an EU citizen" issued under directive 2004/38/EC, which it most likely is not because your wife is German and you live with her in Germany. The permit is therefore most likely governed by German law rather than by EU law, in which case it does not allow you to avoid the visa requirement.
If you do need a visa, or even if you don't, and if you will be traveling with your wife or joining her in the UK, you can apply for an EEA family permit, which is free and supposed to be granted quickly. The criteria for refusal are far more restricted than those for a visitor visa.
If you will neither be traveling with your wife nor joining her in the UK, then you will have to apply for a standard visitor visa instead.