Programmatically, here's a demonstration of how to do this for 1000Genome SNPs on chrY.

First, start with a sorted set of genes in BED format:

$ sort-bed unsorted_genes.bed > genes.bed

(If you don't have locations of your genes, just edit your question to describe what you have, which we can probably work into a BED file.)

Then map 1000Genome SNPs to those genes:

$ wget -qO- ftp://ftp-trace.ncbi.nih.gov//1000genomes/ftp/release/20130502/ALL.chrY.phase3_integrated.20130502.genotypes.vcf.gz \
    | gunzip --stdout - \
    | convert2bed -i vcf - \
    | awk '{print "chr"$0;}' - \
    | bedmap --echo --echo-map-id-uniq --chrom chrY genes.bed - \
    > answer.chrY.bed

This uses convert2bed to convert VCF to sorted BED, and BEDOPS bedmap --echo-map-id-uniq to map a unique list of SNP IDs to each gene in genes.bed.

We add --chrom chrY to bedmap in order focus file operations on the part of the file we're interested in, which improves performance.

The awk statement prepends each line of the BED output with the string "chr", to reformat the chromosome name to UCSC standards, which is the naming scheme used in GENCODE records pulled in the second answer in this post. We want to make sure the chromosome names line up when mapping genes to SNPs.

This is just for chrY. You could probably parallelize this for the other human chromosomes pretty easily (see: www.biostars.org/p/63816/ for other examples):

$ parallel "wget -qO- ftp://ftp-trace.ncbi.nih.gov//1000genomes/ftp/release/20130502/ALL.{}.phase3_integrated.20130502.genotypes.vcf.gz | gunzip --stdout - | convert2bed -i vcf - | awk '{print \"chr\"$0;}' | bedmap --echo --echo-map-uniq-id --chrom {} genes.bed - > answer.{}.bed"::: {1..22} X Y

Then collate the per-chromosome results into one file:

$ bedops --everything answer.*.bed > answer.bed

You can use the Ensembl Perl API.