  The extreme electric fields created in high-intensity laser-plasma
interactions could generate energetic ions far more compactly than traditional
accelerators. Despite this promise, laser-plasma accelerators have remained
stagnant at maximum ion energies of 100 MeV/nucleon for the last twenty years.
The central challenge is the low charge-to-mass ratio of ions, which has
precluded one of the most successful approaches used for electrons: laser
wakefield acceleration. Here we show that a laser pulse with a focal spot that
moves transverse to the laser propagation direction enables wakefield
acceleration of ions to GeV energies in underdense plasma. Three-dimensional
particle-in-cell simulations demonstrate that this relativistic-intensity
"transverse flying focus" can trap ions in a comoving electrostatic pocket,
producing a monoenergetic collimated ion beam. With a peak intensity of
$10^{20}\,$W/cm$^2$ and an acceleration distance of $0.44\,$cm, we observe a
proton beam with $23.1\,$pC charge, $1.6\,$GeV peak energy, and $3.7\,$%
relative energy spread. This approach allows for compact high-repetition-rate
production of high-energy ions, highlighting the capability of more generalized
spatio-temporal pulse shaping to address open problems in plasma physics.
