I don't think a tool exists to do this specifically in RNA-seq data. You could try CalculateFingerprintMetrics from Picard; but the issue is that the genotype assignments could be distorted by unequal expression of alleles. Luckily the approach is pretty straightforward:

after bcftools -C, you can extract the log-odds for each .bam from the GL field. For microarray entries that are hom-ref, use the reference likelihood (remember to normalize the probabilities! 0,4,8 -> -0.442 ref likelihood - natural log); for those that are not, use log(exp(het)+exp(homvar)) which is the non-reference probability (more stable than het or hom as RNA-seq may not have 50/50 allelic expression). Summing these values across all variants will give you a "match likelihood" for each (bam, microarray) pair.