Yes, you can get food poisoning from eating reheated rice. It's not the reheating that causes the problem, but the way the rice has been stored before it's reheated.
How does reheated rice cause food poisoning?
Uncooked rice can contain spores of Bacillus cereus, a bacterium that can cause food poisoning. The spores can survive when rice is cooked.
If rice is left standing at room temperature, the spores can grow into bacteria. These bacteria will multiply and may produce toxins (poisons) that cause vomiting or diarrhoea.
The longer cooked rice is left at room temperature, the more likely it is that the bacteria or toxins could make the rice unsafe to eat.
Symptoms of food poisoning
If you eat rice that contains Bacillus cereus bacteria, you may be sick and experience vomiting or diarrhoea about 1 to 5 hours afterwards. Symptoms are relatively mild and usually last about 24 hours.
Tips on serving rice safely
Ideally, serve rice as soon as it has been cooked. If that isn't possible, cool the rice as quickly as possible (ideally within 1 hour). Keep rice in the fridge for no more than 1 day until reheating. When you reheat any rice, always check the dish is steaming hot all the way through. Do not reheat rice more than once.