What color do orange and purple make?
Orange and Purple make rust.

Orange and Purple make rust, #b62d25. That is the result in equal parts, mixing pigment rather than light - paint, ink and dye all behave this way.
Equal parts orange and purple · #b62d25
Change the ratio
Very little of a mix is ever half and half. Shifting the balance moves the result along the range between the two colours.
3 parts orange, 1 part purple · #d8510c
Equal parts · #b62d25
1 part orange, 3 parts purple · #98124c
Lighter and darker
With white added - a tint · #db9692
With black added - a shade · #6d1b16
Why it works
Pigment mixes subtractively: orange paint absorbs the wavelengths it is not reflecting, purple absorbs its own set, and rust is what neither of them absorbed. This is why paint behaves differently from a screen, where light adds together instead.
Frequently asked questions
What color do orange and purple make?
Orange and Purple make rust, #b62d25. Mixed in equal parts that is the result you get with paint, ink or any other pigment.
How do I make the result lighter or darker?
Add white for a tint - here that gives tan. Add black for a shade, which gives maroon. Add white a little at a time, because it takes far less than people expect to shift a mix.
What happens if I use more orange than purple?
Three parts orange to one part purple gives rust. Reversing it to one part orange and three parts purple gives purple instead.
Does this work the same way on a screen?
No. Screens mix light additively, so red and green light make yellow there. These results are subtractive - paint, ink, dye and pigment - which is what people mean when they ask what two colours make.