  We show that the simplest of existing molecules -- closed-shell diatomics not
interacting with one another -- host topological charges when driven by
periodic far-off-resonant laser pulses. A periodically kicked molecular rotor
can be mapped onto a ''crystalline'' lattice in angular momentum space. This
allows to define quasimomenta and the band structure in the Floquet
representation, by analogy with the Bloch waves of solid-state physics.
Applying laser pulses spaced by $1/3$ of the molecular rotational period
creates a lattice with three atoms per unit cell with staggered hopping. Within
the synthetic dimension of the laser strength, we discover Dirac cones with
topological charges. These Dirac cones, topologically protected by reflection
and time-reversal symmetry, are reminiscent of (although not equivalent to)
that seen in graphene. They -- and the corresponding edge states -- are broadly
tunable by adjusting the laser strength and can be observed in present-day
experiments by measuring molecular alignment and populations of rotational
levels. This paves the way to study controllable topological physics in
gas-phase experiments with small molecules as well as to classify dynamical
molecular states by their topological invariants.
