The intergalactic medium (IGM) plays an important role in the formation and evolution of galaxies. Recent developments in upcoming radio telescopes are starting to open up the possibility of making a first direct detection of the 21 cm signal of neutral hydrogen (H I) from the warm gas of the IGM in large-scale filaments. The cosmological hydrodynamical EAGLE simulation is used to estimate the typical IGM filament signal. Assuming the same average signal for all filaments, a prediction is made for the detectability of such a signal with the upcoming mid-frequency array of the Square Kilometer Array (SKA1-mid) or the future upgrade to SKA2. The signal to noise (S/N) then only depends on the size and orientation of each filament. With filament spines inferred from existing galaxy surveys as a proxy for typical real filaments, we find hundreds of filaments in the region of the sky accessible to the SKA that can be detected. Once the various phases of the SKA telescope become operational, their own surveys will be able to find the galaxies required to infer the position of even more filaments within the survey area. We find that in 120 h, SKA1-mid/SKA2 will detect HI emission from the strongest filaments in the field with an S/N of the order of 10 to similar to 150 for the most pessimistic model considered here. Some of the brighter filaments can be detected with an integration time of a few minutes with SKA1-mid and a few seconds with SKA2. Therefore, SKA2 will be capable of not only detecting but also mapping a large part of the IGM in these filaments.