Yes, it is possible for a man to experience what is called empathic pregnancy or Couvade syndrome during his partner's gestation. It comes from the French word couver, which means incubate or create.
Men present symptoms similar to those of women, such as abdominal pain, mood swings, nausea, vomiting, fatigue and weight gain, among others. Symptoms often cease at the time of delivery, so the only cure is the birth of the baby.
Suggested for you: What Are the Most Common Symptoms of Pregnancy?.