Is there any way to install IOS 13 on my iPad Air?

The original iPad Air can only be updated to iOS12.4.6.

Apple formally ended update support for iPad Air1 in September 2019. Your iPad Air1 cannot be updated to iPadOS13 as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed.

if you want or need to access most current Apps, for which compatibility requires iPadOS 13, you’ll need to consider replacement of your iPad with a newer or current model.

If it is the first generation iPad Air, no. iOS 12.4.6 is the latest iOS that can run on that iPad Air. That is a 7 year old device, and it does not have the ability to run iOS 13.

No.

iOS 12.x.x will be the farthest the 2013, 1st gen iPad Air will ever go.

Sorry.