The eccentricity matrix ɛ ( G ) of a strongly connected digraph G is defined as ɛ ( G ) i j = d ( v i , v j ) , if d ( v i , v j ) = min { e + ( v i ) , e − ( v j ) } , 0 , otherwise . , where e + ( v i ) = max { d ( v i , v j ) ∣ v j ∈ V ( G ) } is the out-eccentricity of the vertex v i of G , and e − ( v j ) = max { d ( v i , v j ) ∣ v i ∈ V ( G ) } is the in-eccentricity of the vertex v j of G . The eigenvalue of ɛ ( G ) with the largest modulus is called the eccentricity spectral radius of G . In this paper, we obtain lower bounds for the eccentricity spectral radius among all join digraphs with a fixed dichromatic number. We also give upper bounds for the eccentricity spectral radius of some special join digraphs with a fixed dichromatic number.