There is no direct connection from Roppongi Station to Shibuya Eki. However, you can take the subway to Aoyama-Itchome then take the Metro to Shibuya. Alternatively, you can take the Metro to Naka-Meguro then take the train to Shibuya.
From Roppongi subway to Aoyama-Itchome then Metro to Shibuya. 9 min ¥391. From Roppongi Metro to Naka-Meguro then train to Shibuya. 14 min ¥292. From Roppongi Station taxi to Shibuya Eki. 5 min ¥3659. From Roppongi Station Uber to Shibuya Eki. 5 min ¥4176. From Roppongi Station walk to Shibuya Eki. 39 min.