Relatively few studies have examined the link between SNPs and mRNA translation, despite the established importance of translational regulation in shaping cell phenotypes. We developed a pipeline analyzing the allelic imbalance in total and polysome-bound mRNAs from paired RNA-seq data of HCT116 cells and identified 40 candidate tranSNPs, i.e. SNPs associated with allele-specific translation. Among them, the SNP rs1053639 (T/A) on DNA damage-inducible transcript 4 (DDIT4) 3UTR was identified, with the reference T allele showing a higher polysome association. rs1053639 TT clones generated by genome editing exhibited significantly higher DDIT4 protein levels than AA ones. The difference in DDIT4 proteins was even greater when cells were treated with Thapsigargin or Nutlin, two perturbations that induce DDIT4 transcription. The RNA binding protein RBMX influenced this allele-dependent differences in DDIT4 protein expression, as shown by RNA-EMSA, RIP, and smiFISH assays. RBMX depletion reduced DDIT4 protein in TT clones to the AA levels. Functionally, TT clones more effectively repressed mTORC1 under ER stress, while AA clones outcompeted TT clones in vitro or when injected in zebrafish embryos. The rs1053639 AA genotype, under a recessive model, correlates with poor prognosis in TCGA cancer data.