Rank in order that List appears

Is there a way I can take 2 lists that contain the same information, and rank it in the order it appears in List B?
So If cell A2 = a1 and cell C4=a1 then cell B2 = 3rd


List A Rank List B
a1 3rd a10
a2 4th a3
a3 2nd a1
a4 10th a2
a5 5th a5
a6 9th a8
a7 8th a9
a8 6th a7
a9 7th a6
a10 1st a4

numbers can be 5, 6, 7, or 8 digits long, also this example is small I will be working with hundreds of number combinations.