I have a dataframe with some columns like this:
A B C
0
4
5
6
7
7
6
5
The possible range of values in A are only from 0 to 7>
IIUC, if you make your (unfortunately named) List into an ndarray, you can simply index into it naturally.
>>> import numpy as np
>>> m = np.arange(16)*10
>>> m[df.A]
array([ 0, 40, 50, 60, 150, 150, 140, 130])
>>> df["D"] = m[df.A]
>>> df
A B C D
0 0 NaN NaN 0
1 4 NaN NaN 40
2 5 NaN NaN 50
3 6 NaN NaN 60
4 15 NaN NaN 150
5 15 NaN NaN 150
6 14 NaN NaN 140
7 13 NaN NaN 130
Here I built a new m, but if you use m = np.asarray(List), the same thing should work: the values in df.A will pick out the appropriate elements of m.
Note that if you're using an old version of numpy, you might have to use m[df.A.values] instead-- in the past, numpy didn't play well with others, and some refactoring in pandas caused some headaches. Things have improved now.