Research in Cooperative Intersection Management (CIM), utilizing Vehicle-to-Everything (V2X) communication among Connected and/or Autonomous Vehicles (CAVs), is crucial for enhancing intersection safety and driving experience. CAVs can transceive basic and/or advanced safety information, thereby improving situational awareness at intersections. The focus of this study is on unsignalized intersections, particularly Stop Controlled-Intersections (SC-Is), where one of the main reasons involving crashes is the ambiguity among CAVs in SC-I crossing priority upon arriving at similar time intervals. Numerous studies have been performed on CIM for unsignalized intersections based on centralized and distributed systems in the presence and absence of Road-Side Unit (RSU), respectively. However, most of these studies are focused towards replacing SC-I where the scheduler provides spatio-temporal or sequence-based reservation to CAVs, or where it controls CAVs via kinematic commands. These methods cause CAVs to arrive at the intersection at non-conflicting times and cross without stopping. This logic is severely limited in real-world mixed traffic comprising human drivers where kinematic commands and other reservations cannot be implemented as intended. Thus, given the existence of SC-Is and mixed traffic, it is significant to develop CIM systems incorporating SC-I rules while assigning crossing priorities and resolving the related ambiguity. In this regard, we propose a distributed Automated Right-of-Way (AROW) algorithm for CIM to assign explicit SC-I crossing turns to CAVs and mitigate hazardous scenarios due to ambiguity towards crossing priority. The algorithm is validated with extensive experiments for its functionality, scalability, and robustness towards CAV non-compliance, and it outperforms the current solutions.