You can do this using R and biomaRt. Here's an example.
First lets create two example sets of SNPS. Between these the first pair are identical, the second pair are synonyms to each other, and the third pair are distinct.
snps1 <- c('rs4844600', 'rs4266886', 'rs6656401')
snps2 <- c('rs4844600', 'rs61737012', 'rs386638846')
Next we load the biomaRt package, and query the variation mart to return all the synonyms and their sources for our first set of rsIDs.
## use the Ensembl variation mart
snp_mart <- useMart(biomart="ENSEMBL_MART_SNP",
## get the synonyms and their source for our SNPs
results <- getBM(filters = c('snp_filter'),
attributes = c('refsnp_id','synonym_name','synonym_source'),
values = snps1,
mart = snp_mart)
For reference, the first few rows of
results looks like the below. You can filter at this stage if you know you only have synonyms from a certain source.
refsnp_id synonym_name synonym_source
1 rs4266886 rs61198255 Archive dbSNP
2 rs4266886 NM_000651.4:c.487+787T>C dbSNP HGVS
3 rs4266886 NM_000573.3:c.487+787T>C dbSNP HGVS
4 rs4844600 rs58362463 Archive dbSNP
5 rs4844600 rs61737012 Archive dbSNP
6 rs4844600 NP_000564.2:p.Glu60= dbSNP HGVS
We can now combine our original set of rsIDs with their synonyms.
snps1_complete <- c(snps1, unique(results$synonym_name))
and then ask which of our second list of IDs is in this expanded list. We see it finds two entries as expected.
> snps2[snps2 %in% snp1_complete]
 "rs4844600" "rs61737012"