Context : The detection of quasi-periodic variability in active galactic nuclei ( AGNs ) in general , and in blazars in particular , is key to our understanding of the origin and nature of these objects as well as their cosmological evolution . PG 1553+113 is the first blazar showing an approximately two-year quasi-periodic pattern in its \gamma -ray light curve , which is also revealed at optical frequencies . Aims : Such quasi-periodicity might have a geometrical origin , possibly related to the precessing nature of the jet , or could be intrinsic to the source and related to pulsational accretion flow instabilities . In this work we investigate and characterise the high-resolution radio emission properties of PG 1553+113 on parsec scales in order to differentiate between these different physical scenarios . Methods : We monitored the source with the very long baseline array ( VLBA ) at 15 , 24 , and 43 GHz during an entire cycle of \gamma -ray activity in the period 2015–2017 , with a cadence of about 2 months , both in total and polarised intensity . We constrained the jet position angle across the different observing epochs by investigating the total intensity ridge lines . Results : We find a core-dominated source with a limb-brightened jet structure extending for \sim 1.5 mas in the northeast direction whose position angle varies in time in the range \sim 40 ^ { \circ } -60 ^ { \circ } . No clear periodic pattern can be recognized in the VLBA light curves during 2015–2017 or in the 15 GHz Owens Valley Radio Observatory light curve during the period 2008–2018 . The core region polarisation percentage varies in the range \sim 1 - 4 \% , and the polarisation angle varies from being roughly parallel to roughly transverse to the jet axis . We estimate a rotation measure value in the core region of \sim - 1.0 \pm 0.4 \times 10 ^ { 4 } rad m ^ { -2 } . The brightness temperature ( T _ { B } ) is found to decrease as the frequency increases with an intrinsic value of \sim 1.5 \times 10 ^ { 10 } K and the estimated Doppler factor is \sim 1.4 . Conclusions : Although the jet wobbling motion indicates that geometrical effects can produce an enhanced emission through the Doppler boosting modulation , additional mechanisms are required in order to account for the quasi-periodic variability patterns observed in \gamma rays . The intrinsic T _ { B } value indicates that the total energy in the core region is dominated by the magnetic field .