A procedure analogous to the Wilcoxon signed-rank test is developed for settings in which ranked-set samples are used in place of simple random samples. The ranked-set sample statistic is shown to be distribution-free and to have a symmetric null distribution. The statistic is a linear combination of U-statistics, so U-statistics results can be used to obtain the asymptotic distribution. Asymptotic relative efficiencies of the test relative to its simple random sample counterpart and to the ranked-set sample sign test are derived. Results are derived for both perfect and imperfect judgment rankings