There has been a lot of promotional merchandise made for Age of Empires over the years. Most of it to date has been available exclusively to Microsoft employees, like what T90 posted.
The Age of Empires community team has had various giveaways with promotional merchandise including the recurring Wololo Wednesday competition, which will return in January 2019.
This past summer the Xbox Official Gear store launched and an Age of Empires t-shirt is currently available for sale. As of this moment, the Age of Empires t-shirt is the only Age of Empires merchandise item available in the Xbox Official Gear store, however I hope that with the upcoming DE releases and AoE IV there will be more Age of Empires merchandise added.