The linear birefringence (LB) of Sr0.61−xBa0.39Nb2O6:Ce 3+ x (SBN61:Ce) has been measured as a function of temperature within the range of 78 ≤ T ≤ 850 K. Large tails have been observed above the ferroelectric phase transition temperatures Tc = 350, 328, 320 and 291 K for the concentrations x = 0, 0.0066, 0.0113 and 0.0207, respectively. Within an Ornstein-Zernike analysis the critical exponents γ, ν and β are determined. It suggests that pure SBN61 belongs to the 3D Ising universality class. Doping with Ce 3+ ions, which seem to act as random fields, enhances the relaxor properties. The critical exponents γ and ν of SBN61:Ce shift against those of the three-dimensional random-field Ising model.