The last MacBook Air to contain a physical reinstallation disk/drive was the 2010 model, which came with a USB flash drive. Subsequent models utilize the built-in Recovery Partition, along with Internet Recovery to enable the user to reinstall the original OS.
If yours is a 2010 model, then you should go through Technical Support to order a replacement drive. It is treated much the same way as if you were ordering a replacement part for your unit.
If you consult an application called MacTracker, you can compare your model as shown in "About this Mac" in the Apple menu, the database in Mactracker to obtain your model# and generation type.