You might attach it to a piece of foam board with double sided tape...

Good idea!

This isn't cheap, but I think it looks this best. (you may be able to find cheaper acrylic frames)

https://wexelart.com/products/40-x-40-floating-acrylic-scarf-frame-1?variant=12468171047014

https://www.etsy.com/shop/HighlandHardware

they have a frameless option:

https://remingtonavenue.com/how-to-frame-a-vintage-hermes-scarf.html

Wow; so many great options! Thank you for your help. I will definitely look into them more seriously.

There are hangers for Japanese furoshiki that would work for this if you can find one long enough.

I found this hanger on Amazon. How would you attach the scarf to the hanger?
https://www.amazon.com/dp/B012DMCTP6/ref=sspa_dk_detail_3?psc=1&pd_rd_i=B012DMCTP6&pd_rd_w=4naq8&pf_rd_p=45a72588-80f7-4414-9851-786f6c16d42b&pd_rd_wg=60ZWs&pf_rd_r=0A5K6V5J30E789KW0WVQ&pd_rd_r=e9aa805c-e78b-4078-b859-444606639d51&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExNjc1SkVaUkpLVEgxJmVuY3J5cHRlZElkPUEwNjUzNjg1UldGVVo3WUlBV1RFJmVuY3J5cHRlZEFkSWQ9QTAwMjI3NzEzUTZSVlBaSTc4QlNCJndpZGdldE5hbWU9c3BfZGV0YWlsJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ==

I would not hesitate to take it to a professional frame shop where they can best deal with a solution.

I'd tack the edges tight over a wood frame.

I would take it to frame shop they will have had lots of experience with textiles Myself I would wear it all the time

I found these wooden magnetic frames online that I am thinking of using. The only bad thing is that it won’t protect the scarf from dust or UV Light. Much cheaper than the acrylic floating frames though.