In this work, we have thoroughly studied the effects of flux composition and temperature on the crystal growth of the BaCu2As2 compound. While Pb and CuAs self-flux produce the well-known {alpha}-phase ThCr2Si2-type structure (Z=2), a new polymorphic phase of BaCu2As2 (b{eta} phase) with a much larger c lattice parameter (Z=10), which could be considered an intergrowth of the ThCr2Si2- and CaBe2Ge2-type structures, has been discovered via Sn flux growth. We have characterized this structure through single-crystal X-ray diffraction, transmission electron microscopy (TEM), and scanning transmission electron microscopy (STEM) studies. Furthermore, we compare this new polymorphic intergrowth structure with the {alpha}-phase BaCu2As2 (ThCr2Si2 type with Z=2) and the b{eta}-phase BaCu2Sb2 (intergrowth of ThCr2Si2 and CaBe2Ge2 types with Z=6), both with the same space group I4/mmm. Electrical transport studies reveal p-type carriers and magnetoresistivity up to 22% at 5 K and under a magnetic field of 7 T. Our work suggests a new route for the discovery of new polymorphic structures through flux and temperature control during material synthesis.