xkcd

Doing some quick math here:

Circumference of the Earth is about 24k mi = 44M yds.

The cheapest fishing line I could find online (from Amazon) (I didn't search very hard though) was $10 for 440 yds of line. To circle the Earth, you'd need 44M / 440 = 100k spools = $1M for the fishing line.

Let's assume every spool needs about 1 kite. That's 100k kites. You can find kites online for like $5 each, but the cheapest way to get a kite is probably to bulk order wooden sticks and plastic film and make them yourself. Let's do the math on that.

Assume each kite requires a generous 5 ft^2 of film, and 10 ft of sticks. I found some bulk plastic film rolls online (from McMaster Carr) for about $0.02 per ft^2, and some wooden marshmellow sticks (on Amazon) for about $0.10 per foot. That makes $0.02*5 + $0.10*10 = $1.10 per kite. That totals $1.10 * 100k = $110k.

So using these estimates, this kite ring costs around $1.11M.

No clue if it would actually work though.

Edit: corrected a math error