We use well resolved numerical simulations with the lattice Boltzmann method to study Rayleigh-Benard convection in cells with a fractal boundary in two dimensions for Pr = 1 and Ra is an element of [10(7), 10(10)], where Pr and Ra are the Prandtl and Rayleigh numbers. The fractal boundaries are functions characterized by power spectral densities S(k) that decay with wavenumber, k, as S(k) similar to kp (p < 0). The degree of roughness is quantified by the exponent p with p < -3 for smooth (differentiable) surfaces and -3 <= p < -1 for rough surfaces with Hausdorff dimension D-f = 1/2 ( p + 5). By computing the exponent beta using power law fits of Nu similar to Ra-beta, where Nu is the Nusselt number, we find that the heat transport scaling increases with roughness through the top two decades of Ra is an element of [10(8), 10(10)]. For p = -3.0, -2.0 and -1.5 we find beta = 0.288 +/- 0.005, 0.329 +/- 0.006 and 0.352 +/- 0.011, respectively. We also find that the Reynolds number, Re, scales as Re similar to Ra-xi, where xi approximate to 0.57 over Ra is an element of [10(7), 10(10)], for all p used in the study. For a given value of p, the averaged Nu and Re are insensitive to the specific realization of the roughness.