Rearranging Inventory in Fallout Shelter
No, you cannot sort your inventory in Fallout Shelter. Items and apparel will be listed in the order they were recovered, crafted, or acquired.
You can sort your dwellers, however, by opening the vault dweller list and selected the "Dwellers" header on the top to sort alphabetically or the "Job" header to sort by their assigned task. This functionality does not exist when viewing your vault's inventory.