No, this is a myth.
It is true that you are exposed to more radiation at higher altitudes, including when you are flying in a plane. However, the level that you’d be exposed to on a single flight in the first trimester is nowhere near high enough to cause birth defects or a miscarriage. One special group who might want to pay more attention are those who fly very frequently, such as flight attendants or people who travel a lot for business. Radiation exposure adds up, so if you fly this much you may want to consider wearing a simple meter that can track your cumulative levels (they are very tiny and clip on your clothes) to know if your levels are getting too high for what we consider safe in pregnancy. Remember, this is only for very frequent fliers!