I take Phenibut myself and yes it can make you feel sleepy and help you fall asleep at times due to the calming effect.
Since I only thought Phenibut was used for my anxiety I asked my doctor if it was normal for me to feel sleepy at times when taking Phenibut and he said it was normal and to avoid taking the Phenibut whenever I plan to drive or operate any machinery.
Phenibut can also be used to cure Insomnia so a doctor may also prescribe Phenibut if you're having trouble sleeping.