To use multiple columns of a dataframe to apply the rank() function, you can provide multiple columns as a list.
The function will return the rank of the data items in those columns. In the following example, I have used the 'first' method in the rank function. It will assign rank in the order they appear in the column.
>>> import pandas as pd
>>> df=pd.DataFrame({'A':[4,6,3,1,8], 'B':[43,12,54,34,67], 'C':[32,45,12,68,43]})
>>> df
A B C
0 4 43 32
1 6 12 45
2 3 54 12
3 1 34 68
4 8 67 43
>>> df[['A','B']].rank(method='first')
A B
0 3.0 3.0
1 4.0 1.0
2 2.0 4.0
3 1.0 2.0
4 5.0 5.0