How can we know when a user is truly collaborating with a machine—and not just using it? With evolving functional capabilities of conversational agents (CAs) such as ChatGPT, users increasingly engage with them not as mere tools but as collaborative partners. This shift raises the question: What contribution do users make to such a collaboration, and how can it be measured? Building on the concept of collaborative intelligence, we developed and validated the CI-Tex Scale, a behavioral scale to measure Collaboration Intensity (i.e., users' degree of engagement with conversational agents in collaborative tasks) in text-based human-CA interactions. Grounded in Item Response Theory, the CI-Tex scale quantifies users' extent of collaborative engagement across different behavioral categories. Based on data from two studies (Total N = 599), CI-Tex emerged as a unidimensional construct with good model fit and high empirical reliability of .87 (Study 1) and .84 (Study 2). A strong correlation with human-voice assistant collaboration intensity (r1 = .57, r2 = .50) supports convergent validity. Moderate correlations with attitudes toward AI (r = .42) and innovativeness (r = .36), as well as a near-zero correlation with AI anxiety (r = -.03) in Study 1, provided evidence of discriminant validity. The scale complements existing technology acceptance measures by focusing on the depth of users' actual collaboration behaviors. Thus, it offers researchers a robust and adaptable tool to assess individual differences in human-CA collaboration and provides practitioners with insights to match users to contexts where collaboration with CAs is necessary.