There is no direct way to do this. There are some methods that seem to allow you define length. For example start, center, length. But this is defining the chord length, not the arch length.
There is a suggestion to calculate the angle using simple mathematic calculation, comparing the arch radius and arch length. After you get the angle value, then you can draw it. But it is not easy.
I suggest a better solution: draw the arch, then modify it using lengthen tool.
Lengthen tool allows you to define the object total length, including an arch. Select the total length option, then type the distance you want.
Select an object or [DElta/Percent/Total/DYnamic]: T
Specify total length or [Angle] <1.0000)>: 1000
Select an object to change or [Undo]:
Now if I try to inquiry or see the arc properties, I will see the arch has the exact length I wanted.