Given the potential for technology to inflict harm and injustice on society, it is imperative that we cultivate a sense of social responsibility among our students as they progress through the Computer Science (CS) curriculum. Our students need to be able to examine the social complexities in which technology development and use are situated. Also, aligning students' personal goals and their ability to achieve them in their field of study is important for promoting motivation and a sense of belonging. Promoting communal goals while learning computing can help broaden participation, particularly among groups who have been historically marginalized in computing. Keeping these considerations in mind, we piloted an introductory Java programming course in which activities engaging students in ethical and socially responsible considerations were integrated across modules. Rather than adding social on top of the technical content, our curricular approach seeks to weave them together. The data from the class suggests that the students found the inclusion of the social context in the technical assignments to be more motivating and expressed greater agency in realizing social change. We share our approach to designing this new introductory socially responsible computing course and the students' reflections. We also highlight seven considerations for educators seeking to incorporate socially responsible computing.