The timing properties of the 4.45 s pulsar in the Be X-ray binary system GRO J1750-27 are examined using hard X-ray data from INTEGRAL and Swift during a Type II outburst observed during 2008. The orbital parameters of the system are measured and agree well with those found during the last known outburst of the system in 1995. Correcting the effects of the doppler shifting of the period, due to the orbital motion of the pulsar, leads to the detection of an intrinsic spin-up that is well described by a simple model including Pdot and Pdotdot terms of -7.5E-10 ss^-1 and 1E-16 ss^-2 respectively. The model is then used to compare the time-resolved variation of the X-ray flux and intrinsic spin-up against the accretion torque model of Ghosh & Lamb (1979); this finds that GRO J1750-27 is likely located 12-22 kpc distant and that the surface magnetic field of the neutron star is ~2E12 G. The shape of the pulse and the pulsed fraction shows different behaviour above and below 20 keV indicating that the observed pulsations are the convolution of many complex components. ; Comment: Accepted for publication in MNRAS. 11 pages, 10 figures and 2 tables