The progenitor systems accounting for explosions of Type Ia supernovae (SNe Ia) is still under debate. Symbiotic channel is one of the possible progenitor scenarios, in which the WDs in these systems increase in mass through wind accretion from their red giant companions. The mass-loss processes of the giants in the symbiotic systems could produce the amount of circumstellar medium (CSM), and detections of interaction signals between SN ejecta and CSM can be used as an ideal way to distinguish different progenitor models. However, the density distribution and geometric structure of the CSM around the symbiotic systems remain highly uncertain. By assuming that the tidal torque from binary interaction can increase the mass-loss rate of the red giant and cause the stellar wind concentrate towards the equatorial plane, we provide a simplified method to estimate the density and the degree of deviation from spherical symmetry for the CSM. Based on the calculations of the binary evolutions of symbiotic systems using stellar evolution code mesa, we obtained the parameter space for producing SNe Ia. We found that SNe Ia could originate from symbiotic systems with massive carbon-oxygen white dwarfs (CO WDs), while the half-opening angle of the stellar wind from red giant towards the WD varies with the binary evolution, resulting in the formation of surrounding CSM with different geometric structures. The corresponding properties of ejecta-CSM interactions may be examined by spectropolarimetry observations in the future, from which one may find an additional relationship between circumstellar environment of SNe Ia and their progenitor systems.