The disk-outflow connection is thought to play a key role in extracting excess angular momentum from a forming proto-star. Though jet rotation has been observed in a few objects, no rotation of molecular outflows has been unambiguously reported so far. We report new millimeter-interferometric observations of the edge-on T Tauri star - disk system in the isolated Bok globule CB26. The aim of these observations was to study the disk-outflow relation in this 1Myr old low-mass young stellar object. The IRAM PdBI array was used to observe 12CO(2-1) at 1.3mm in two configurations, resulting in spectral line maps with 1.5 arcsec resolution. We use an empirical parameterized steady-state outflow model combined with 2-D line radiative transfer calculations and chi^2-minimization in parameter space to derive a best-fit model and constrain parameters of the outflow. The data reveal a previously undiscovered collimated bipolar molecular outflow of total length ~2000 AU, escaping perpendicular to the plane of the disk. We find peculiar kinematic signatures that suggest the outflow is rotating with the same orientation as the disk. However, we could not ultimately exclude jet precession or two misaligned flows as possible origin of the observed peculiar velocity field. There is indirect indication that the embedded driving source is a binary system, which, together with the youth of the source, could provide the clue to the observed kinematic features of the outflow. CB26 is so far the most promising source to study the rotation of a molecular outflow. Assuming that the outflow is rotating, we compute and compare masses, mass flux, angular momenta, and angular momentum flux of disk and outflow and derive disk dispersal timescales of 0.5...1 Myr, comparable to the age of the system.