Single crystals of Ba_{1-x}Rb_{x}Fe_2As_2 with x=0.05-0.1 have been grown from Sn flux and are bulk superconductors with T_c up to 23 K. The crystal structure was determined by X-ray diffraction analysis, and Sn is found to be incorporated for 9% Ba, shifted by 1.1 Angstroem away from the Ba site towards the (Fe_2As_2)-layers. The upper critical field deduced from resistance measurements is anisotropic with slopes of 7.1(3) T/K (H || ab-plane) and 4.2(2) T/K (H || c-axis), sufficiently far below T_c. The extracted upper critical field anisotropy of 3 close to T_c, is in good agreement with the estimate from magnetic torque measurements. This indicates that the electronic properties in the doped BaFe_2As_2 compound are significantly more isotropic than those in the LnFeAsO family. The in-plane critical current density at 5 K exceeds 10^6 A/cm^2, making Ba_{1-x}Rb_xFe_2As_2 a promising candidate for technical applications.
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