A fractional trapezoidal rule type difference scheme for fractional order integro-differential equation is considered. The equation is discretized in time by means of a method based on the trapezoidal rule: while the time derivative is approximated by the standard trapezoidal rule, the integral term is discretized by means of a fractional quadrature rule constructed again from the trapezoidal rule. The solvability, stability and L2-norm convergence are proved. The convergence order is second order both in temporal and spatial directions. Furthermore, a spatial compact scheme, based on the fractional trapezoidal rule type difference scheme, is also proposed and the similar results are derived. The convergence order is second for time and fourth for space. Preliminary numerical experiment confirms our theoretical results