Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type R^2-θ/2 in the effective Lagrangian, where θ>0 is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data puts important constraints on the strength of this new type of couplings.