This paper introduces a soft-error tolerant asynchronous ternary content-addressable memory (TCAM) based on a transistor/magnetic-tunnel-junction (MTJ) hybrid structure. An MTJ device that is often used for a non-volatile memory stores one-bit information as a resistance whose value is robust against alpha particle and atmosphere neutron strikes, which significantly lower the probability of single-event upsets (SEUs). The TCAM is also robust against delay variations caused by single-event transients (SETs) as it is designed based on four-phase dual-rail encoding realized using complementary NAND and NOR-type word circuits. The dual-rail TCAM cell is compactly designed using 20 transistors (20T) and 4 MTJ devices stacked on a CMOS layer as opposed to a single-rail 24T TCAM cell that consists of soft-error tolerant storage elements. In addition, soft errors can be detected using the dual-rail signals. As a design example, a 256-word x 64-bit TCAM is designed under a 90 nm CMOS/MTJ technology and is evaluated with a collected charge caused by a particle strike, which induces the SET and hence the delay variation. The proposed TCAM properly operates under the delay variation, while achieving comparable performance to a synchronous single-rail TCAM in which an up to 25% timing error occurs.