Using the handcuffs, as well as other materials, you will be able to craft the Alligator Tooth Talisman.
This special item can be retrieved starting Chapter 2.
Where to Find the Vintage Civil War Handcuffs:
You can obtain the Vintage Civil War Handcuffs in Red Dead Redemption II after mailing a complete set of Cigarette Cards to Phineas T. Ramsbottom, as part of the Smoking and Other Hobbies Stranger Mission.
To start the said mission, first, you need to complete Who is Not Without Sin. Next, you need to travel to Flatneck Station where you will meet Phineas T. Ramsbottom below.
After Phineas introduces you the Cigarette Cards, you’ll have to find a complete set and mail it to him. You can do that from any post office.
Keep in mind that each set has 12 cards and there is a total of 144 Cigarette Cards in Red Dead Redemption 2.
To get the Vintage Civil War Handcuffs; however, you only need to mail 12 cards from the same set. After 24 in-game hours, check the mail and you will receive the Vintage Handcuffs.
How to Use the Vintage Handcuffs:
After you find the Civil War Handcuffs you can use them at a Fence to craft the Alligator Tooth Talisman. For this talisman, you will also need a Gold Jointed Bracelet and the tooth of a Legendary Alligator.