There is no direct connection from Asakusa to Roppongi Station. However, you can take the subway to Daimon(Tokyo) then take the subway to Roppongi. Alternatively, Tokyo Metro operates a vehicle from Asakusa to Roppongi Station every 10 minutes. Tickets cost $2 - $3 and the journey takes 28 min.
How to get from Asakusa to Roppongi Station
From Asakusa(Tobu/Subway) subway to Daimon(Tokyo) then subway to Roppongi. 26 min ¥458. From Iriya(Tokyo) Metro to Roppongi. 28 min ¥231. From Asakusa(Tsukuba) train to Akihabara then Metro to Roppongi. 30 min ¥426. From Asakusa taxi to Roppongi Station. 10 min ¥7668. From Asakusa drive to Roppongi Station. 10 min ¥230.