What do I use to cap a kitchen sink sprayer hose?
If 3/8" is the correct size, I believe you need a 3/8" FIP cap (FIP stands for Female Iron Pipe) also known as a 3/8" female NPT cap. If the size is actually 1/2", then obviously you'd need in the 1/2" size.

You would also need pipe dope or teflon pipe dealing tape The dope comes in a smaller size in a tube or larger size in a jar. IP does not mean you'd get it in iron or steel. You'd probably get it in brass.