'Increment' means 'add one'. In the context of a pay rise, it means that you go up one step in some sort of formal pay scale.
So - 'an increment' would be appropriate to a job in a government, or large corporation, which has a fixed pay scale, and people move from one pay step to another. It can be possible to get a 'double increment' if you do particularly well.
If the pay system is not regulated like that, you should not use it, and should just use 'rise' or 'increase'.