There is no simple answer to this question, please read the full answer to understand the context where toilet paper is used my Muslims.
Hygiene is extremely important in Islam.
Islamic principles dictate that a Muslim take measures to ensure personal hygiene at all times. The Holy Prophet (Peace Be Upon Him) went so far as to declare that: "Cleanliness is half of Faith".
During the early times, commodities like toilet paper were not available and so the Islamic rules stated one use water to clean themselves up. However, in recent times with the advent of mass production and the common use of Toilet Paper in some societies. Muslim scholars have issued a decree stating that in the absence of water, use of toilet paper, stones/rocks, wood etc is permissible. However, Water is always preferred over toilet paper because it removes all the impurities unlike toilet paper whose use leaves behind residue and so impurities exist and complete cleanliness is not ensured.
So, the use of toilet paper is permitted but Water is highly preferred.