Baby carriers are about a million times more convenient when traveling than strollers, and yes, you can wear them at the airport. However, your baby carrier must be x-rayed at security, so you may be asked to remove it. You must also remove your baby from your carrier during your flight (source).
It’s always a good idea to check with the airport before flying and confirm their policies for children, as these will vary based on the child’s age, the airline, and the destination country.