The short answer is, no. There are a few exceptions in Bangkok, notably at some of the more prestigious hotels, but in the majority of cases tap water is not safe to drink anywhere in Thailand. That’s the bad news, but the good news is that bottled water is extremely cheap and widely available.
Most hotels and guest houses will provide a couple of complimentary bottles of water. There are numerous reputable brands available including Nestle and Singha. Imported water like Evian is also available, but in my opinion doesn’t justify the extra expense when the local alternatives are equally as good. To be extra-cautious, you could also consider using bottled water when brushing your teeth.