Only moderators can pin. Do not give moderator permissions to your entire userbase. Regular users cannot pin activity. This assumes pinning is even enabled within your activity stream. You can check if its globally enabled in CB Activity > Parameters > Activity > Display.
Note pinned activity is deprecated. It will be completely gone in CB Activity 6.0.0. I do not recommend becoming dependent on that feature. The same applies to global posts (announcement button). Both of these features impose a significant performance impact so they are removed in 6.0.0.