Does UV water purification cause cancer?
Is it possible that this use of UV radiation may lead to cancer in humans?


No!

The lamps used for water treatment are usually low pressure mercury vapour lamps. These lamps emit in the UV-C range with a maximum at $\lambda = 254~\mathrm{nm}$.


No mercury can escape from an intact lamp. 
In principle, UV-C radiation may cause severe sun burns and harm your eyes. However, the lamps are housed and the consumer is protected from the direct exposure to radiation.
There is no change to the water due to UV irradiation.
UV-C radiation is efficient in killing microorganisms in water.