Coated conductor tapes are promising materials for the construction of high field inserts ( 20 T). In a magnet, the magnetic field at the coil ends is not parallel to the wide face of the tape, and the angle can reach values larger than 10 degrees. Coated conductors have very anisotropic transport properties, thus it is very important to measure the angular dependence of the critical current. The critical current of commercial YBCO coated conductors made by SuperPower has been measured at 12 T, 4.2 K as a function of the angle between the magnetic field and the wide face of the tape, with a precision of less than 0.2 degree. The experimental results have been used for designing insert coils for high field magnets: depending on the coil parameters and current, the high sensitivity to the magnetic field angle of YBCO tape can affect the performances of the coil.