ABSTRACT Quasars at redshifts z > 6 are an excellent probe of the formation and evolution of supermassive black holes in the early Universe. The population of radio-luminous quasars is of particular interest, as such quasars could potentially be used to study the neutral intergalactic medium during cosmic reionization via H i 21 cm absorption studies. However, the lack of deep radio observations of z > 6 quasars leaves the population poorly constrained, and suitable candidates for an H i 21 cm absorption study have yet to be found. In this work, we present Jansky Very Large Array (VLA) 1–2 GHz radio continuum observations of 138 quasars at redshifts 6.0 ≤ z < 7.6. We detect the radio continuum emission of the z = 6.1 quasar J1034−1425, with a 1.6 GHz flux density of $170\pm 36\, \mu$Jy. This quasar is radio-quiet with radio-loudness, R ≡ f5 GHz/fν, 4400 Å = 2.4 ± 0.5. In addition, we detect seven other quasars at z > 6, which have previously been characterized in the literature at these frequencies. Using the full sample, we estimate the radio-loud fraction to be $3.8^{+6.2}_{-2.4}\ \hbox{per cent}$, where the uncertainties are 95 per cent confidence intervals. This is lower than recent estimates of the radio-loud fraction in the literature, but is still marginally consistent with no redshift evolution of the radio-loud fraction. We explore the undetected quasar population by stacking their continuum images at their optical positions and obtain a median stacked flux density of 13.8 ± 3.9 µJy and luminosity of log L5 GHz/(W Hz−1) = 24.2 ± 0.1.