Are you talking about at the time of Earth's formation, as in, early Earth gets a magnetic field, which attracts more iron and nickel to the core as it's forming? That seems unlikely, since the Earth's magnetic field is caused by convection currents of iron around the core, which requires the immense heat and pressure of an entire rocky planet around it to work. (But I don't know.)

Are you instead asking whether metal would be attracted to Earth since after Earth's formation through today? In short, yes. Our magnetic field has components both inward toward the core and parallel to the Earth's surface. On the surface we humans mostly can see the effects of the magnetic field as exerting a force on a compass needle. The needle is very light, carefully balanced, and shielded from the air so that there are as few additional forces involved that could overwhelm or resist that caused by Earth's magnetic field. Also, a compass needle is magnetized so that it aligns correctly and at maximum force with magnetic North. In principle a non-magnetized iron (or other ferromagnetic) needle can also be used in a compass, following recalibration. [See a StackX explanation on this, though the answer appears to be interpreting the necessary energy as that needed to permanently magnetize a needle, as opposed to simply the Zeeman energy, which is a net gain when the sum of alignment directions of its tiny component magnetized crystals with respect the external magnetic field is calculated. Thus as long as resistance in the compass chamber is minimal, the needle should eventually align. Magnetite as lodestone, incompletely magnetized, was used in this way.]

Note that in orbit the magnetic field is only about half as strong as on the surface (where it is already quite weak by human observation standards), and it decreases steeply further out, but low orbit is perhaps the first place where you might first think of a free unmagnetized iron or nickel (a ferromagnetic metal) object being noticeably affected by Earth's magnetic field. There's a lot of subtleties here that I'm sure I'll miss, but let's try a calculation: taking magnetic saturation into account (thanks u/mfb- ), the max magnetization of steel is 2 T, and if we have a 1 m^3 block of steel in space then that's a magnetic dipole moment of 2 A m^2, so with a magnetic field in orbit of 35 * 10^(-6) T, the forces experienced in orbit are at max 7 * 10^(-5) N. Compare this to, say, the total drag forces in orbit, say at ISS orbit at 400 km (p. 14) ~ .001 dynes/cm^2 * 100^2 cm^2 * 10^(-5) N/dyne = 10^(-4) N. So at most, the magnetic forces on this (unrealistically) enormous metal block in orbit would be of comparable magnitude, a bit less, than the not insignificant drag at the ISS, which is more significant than I expected if I took into account everything needed (which is a big "if").