Can you integrate an electromagnetic coil (torque rod) to a PCB design in EAGLE?
You can integrate coils into the PCB, yes. Is it efficient? No.

Q-factor of PCB inductors is generally lowered then Q-factor of the
inductors having a coil of wire and less than that of the cylindrical
microstrip coils. The self-capacitance of the printed inductors
depends on the width of the spiral turns, the gap between them and the
PCB material and can reach 3 to 5 pF, which is pretty high at such
frequencies

Source: https://coil32.net/pcb-coil.html
The magnetic moment is a factor of the number of turns, the current and the area. So many torquer coils are simply rectangles built into one or more layers of the PCB.
m = nAI
More turns are easier to create with wire, which has a much higher packing factor for current carrying wires than a PCB (or flat flex), because enamel is much smaller than layers of a PCB or flat flex. It really depends on the magnetic moment needed, if you need a high magnetic moment, then you might have to resort to wire outside of the PCB, because most PCB's are fabricated with 4 layers (you can do more, but it comes with a cost).
If you do wish to create a magnetorquer on a PCB, eagle (or any PCB software), just draw the pattern out by hand in the software.
In the design I used for a magnetorquer (which flew) I personally wound a rectangular delrin frame with about 400 turns, which was then fastened to 4 posts on the PCB. The wire was soldered into vias. I remember that the other 2 torquer coils were built into the solar panel arrays.
Here is a paper describing a satellite with coils built in to the PCB with copper traces forming the coil:

Source: Innovative power management ADCS