If it interacts
only gravitationally, the answer is that probably we will never detect a dark matter particle.
However, good news: several possible dark matter particles have been proposed, all of which interact very very slightly non-gravitationally as well. Practically all such proposals start with a particle physicist trying to repair some problems in the standard model of particle physics. When such proposed particles are decent candidates for cold dark matter, astrophysicists and physical cosmologists take note.
One family of candidates are the WIMPs, which feel the weak force, and so can produce a recoil reaction in atomic nuclei, and we can spot such recoils produced by neutrinos sourced by the sun or nuclear reactors. Galactic dark matter doesn't have a "bright spot" like the sun or the Super Kamiokande reactor, so distinguishing recoils from Brownian motion is tricky, since a WIMP may enter a recoil-detector from any direction. The density of WIMPs (if they exist) is much lower than the neutrinos streaming out of SK reactor or the sun, so there will be fewer recoils in the first place. WIMPs are generally found in various attempts to explain chirality in the standard model.
Another family of particle-physics-problem-solving dark matter candidates are the axions which feel both the strong and weak forces, and axions can be smashed up into photons (or formed from photons) in a very strong magnetic field.
There are several much less popular hypothesized particles that can be detected in principle because they feel one of the non-gravitational fundamental forces. This does not mean it is easy to detect them, though: whatever the microscopic makeup of dark matter, it is very sparse inside the solar system, and galactic dark matter reaches Earth with relatively low momentum, so even when it does interact with ordinary matter on Earth, it won't produce a large reaction.
> orbiting with crazy speeds around our planet
Galactic dark matter particles must move with the rotation of the galaxy, and for the most part so does our whole solar system, so the speeds will be slow, and in particular not at all relativistic. Also, because dark matter forms a dust where the individual bits of dust have extremely low mass, they will not be drawn into orbit around the Earth. The dark matter particles' orbits around the centre of the galaxy will be very slightly perturbed by the Earth, though.