First, the best news: Every season of "Blue Bloods," including the episodes in the current Season 12, can be streamed by Paramount+ subscribers. Additionally, if you subscribe to the Paramount+ channel on Amazon Prime Video, you will also be able to commit to a mega-binge watch of the CBS drama. Paramount+ is CBS' official streaming platform, formerly called "CBS All Access" before its rebrand in 2021 (via /Film).
If you don't have Paramount+, you can always sign into the CBS site with your TV provider credentials and watch all episodes of "Blue Bloods" there. CBS offers a detailed explanation of how to go about that on its website help center. Alternatively, if neither of those options works for you, there are still a few potential avenues. All 12 seasons are available for purchase as individual titles on Prime Video, Apple TV+, Google Play, and Vudu. You can also buy individual episodes or entire season bundles on those services if you want to break up your "Blue Bloods" marathon into smaller pieces.
And, if that doesn't work, Hulu currently has the first nine seasons of "Blue Bloods" in its catalog. If you're a Hulu subscriber, those seasons — which collectively add up to 199 episodes — should certainly be enough to tide you over until more options become available.