We investigated the effect of the torsional rigidity of a semiflexible chain on the wrapping transition around a spherical core, as a model of a nucleosome, the fundamental unit of chromatin. Through molecular dynamics simulation, we show that the torsional effect has a crucial effect on the chain wrapping around the core under the topological constraints. In particular, the torsional stress (i) induces the wrapping/unwrapping transition, and (ii) leads to a unique complex structure with an antagonistic wrapping direction which never appears without the topological constraints. We further examine the effect of the stretching stress for the nucleosome model in relation to the unique characteristic effect of the torsional stress on the manner of wrapping.