Use Lower In-Game Sensitivity and Higher Mouse DPI
In-game sensitivity controls how fast you turn in the game. This value is set inside your game, usually in the options menu under input. Sometimes only a slider with no values is shown in the menu, but you can usually set an exact value by using the game's console or configuration files. Each game handles sensitivity values in its own way but a lower sensitivity allows more precise movements, so it is usually best to set the in-game sensitivity to as low of a value as possible and increase your mouse DPI to get the speed you want. However, in some games if sensitivity values are set to fractions there can be rounding errors leading to less precise movements.
A 1.0 in-game sensitivity will typically yield the most precise mouse movement the game engine can handle. I recommend you set your in-game sensitivity to 1.0 then adjust your DPI until you get a speed you are comfortable with. If you still need faster turning speed after maxing out your DPI increase your in-game sensitivity.