Strong laser-driven magnetic fields are crucial for high-energy-density physics and laboratory astrophysics research, but generation of axial multikilotesla fields remains a challenge. The difficulty comes from the inability of a conventional linearly polarized laser beam to induce the required azimuthal current or, equivalently, angular momentum (AM). We show that several laser beams can overcome this difficulty. Our three-dimensional kinetic simulations demonstrate that a twist in their pointing directions enables them to carry orbital AM and transfer it to the plasma, thus generating a hot electron population carrying AM needed to sustain the magnetic field. The resulting multikilotesla field occupies a volume that is tens of thousands of cubic microns and it persists on a picosecond timescale. The mechanism can be realized for a wide range of laser intensities and pulse durations. Our scheme is well suited for implementation using multikilojoule petawatt-class lasers, because, by design, they have multiple beamlets and because the scheme requires only linear polarization.