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Polygnicity refers to the phenomenon that multiple genetic variants have a non-zero effect on a complex trait. It is defined as the proportion of genetic variants that have a nonzero effect on the trait. Evaluation of polygenicity can provide valuable insights into the genetic architecture of the trait. Several recent works have attempted to estimate polygenicity at the SNP level. However, evaluating polygenicity at the gene level can be biologically more meaningful. We propose the notion of gene-level polygenicity, defined as the proportion of genes having a non-zero effect on the trait under the framework of transcriptome-wide association study. We introduce a Bayesian approach polygene to estimate this quantity for a trait. The method is based on spike and slab prior and simultaneously provides an optimal subset of non-null genes. Our simulation study shows that polygene efficiently estimates gene-level polygenicity. The method produces downward bias for small choices of trait heritability due to a non-null gene, which diminishes rapidly with an increase in the GWAS sample size. While identifying the optimal subset of non-null genes, polygene offers a high level of specificity and an overall good level of sensitivity -- the sensitivity increases as the sample size of the reference panel expression and GWAS data increase. We applied the method to seven phenotypes in the UK Biobank, integrating expression data. We find height to be most polygenic and asthma to be the least polygenic. Our analysis suggests that both HDL and triglycerides are more polygenic than LDL.