Governed by the hairy ball theorem, classical antennas with isotropic responses to linearly polarized radio waves are unrealizable. Also, their calibrations face a causal dilemma. Therefore, radio wave measurements based on classical antennas are challenging to achieve high accuracy. This work shows that the antenna based on Rydberg atoms can theoretically achieve an ideal isotropic response to linearly polarized radio waves; that is, it has zero isotropic deviation. Although this conclusion is straightforward, it is not theoretically clear when complex atomic energy levels are taken into account. Experimental results of isotropic deviation within 5 dB and 0.3 dB possible with optimization in microwave and terahertz wave measurements support the theory and is at least 15 dB improvement than the classical omnidirectional antenna. Combined with the SI traceable and ultrawideband property, the ideal isotropic response will make radio wave measurement based on atomic antenna much more accurate and reliable than the traditional method. This isotropic atomic antenna is an excellent example of what a tailored quantum sensor can realize, but a classical sensor cannot. It has crucial applications in fields such as radio wave electrometry.