Most journals have a list of features that help you determine what kind of articles they accept. Check these things out first to see if it is a good publication venue for you:
When you get ready to submit, follow the journal's instructions to the letter.
Dartmouth Law Journal
We welcome any submissions by graduate or law students, law professors, and legal practitioners. Undergraduate students may submit shorter pieces to DLJ Online, the Journal's blog (http://dartmouthlawjournal.org/dljonline/).
Dialectics: Journal of Law, Leadership, and Society
Online journal devoted to undergraduate scholarship and discourse, ... "accepting high quality essays on issues of public importance. We search for papers that have a single thesis, are focused, identify significant societal and global issues, and offer creative solutions or specific recommendations for addressing the challenges."
International Social Science Review
Journal of Pi Gamma Mu International Honor Society. Accepts manuscripts in archaeology, public health, history, political science, sociology, anthropology, economics, international relations, criminal justice, social work, psychology, social philosophy, history of education, human/cultural geography, and all social science interdisciplinary fields.
Penn Undergraduate Law Journal
"PULJ will only accept written works by undergraduate students. We accept a wide array of submission types, including, but not limited to: research papers, senior theses, and independent projects or studies. Given the interdisciplinary focus of our publication, students in any field of study are welcome to submit their work, so long as their piece relates to law or the legal system."
Washington University Undergraduate Law Review
Student-run journal featuring research papers from undergraduate students across the United States.