We report the first statistical detection of X-ray emission from cosmic web filaments in ROSAT data. We selected 15 165 filaments at 0.2 <   z  <  0.6 ranging from 30 Mpc to 100 Mpc in length, identified in the Sloan Digital Sky Survey survey. We stacked the X-ray count-rate maps from ROSAT around the filaments, excluding resolved galaxy groups and clusters above the mass of ∼3 × 10 13   M ⊙ as well as the detected X-ray point sources from the ROSAT, Chandra , and XMM-Newton observations. The stacked signal results in the detection of the X-ray emission from the cosmic filaments at a significance of 4.2 σ in the energy band of 0.56−1.21 keV. The signal is interpreted, assuming the Astrophysical Plasma Emission Code model, as an emission from the hot gas in the filament-core regions with an average gas temperature of 0.9 −0.6 +1.0 keV and a gas overdensity of δ  ∼ 30 at the center of the filaments. Furthermore, we show that stacking the SRG/eROSITA data for ∼2000 filaments only would lead to a ≳5 σ detection of their X-ray signal, even with an average gas temperature as low as ∼0.3 keV.