Is there a blood test to see if you're a carrier for downs syndrome?

Yes. The features of down syndrome can be passed by a carrier (someone with a piece of a 21 chm in a balanced swap with another chm).The egg/sperm of that individual may pass extra 21 material & conceive a ' translocation down syn ' which makes up <2% of ds. Ds is not carried like sickle cell or cystic fibrosis inbedded in genes.If your chms are nl your risk is that of the population & more age related.
Yes. Since almost all cases of down syndrome (maybe 95-98% of cases) are not inherited from carrier parents, the testing of the parents' chromosomes is probably not done unless a down syndrome baby has been born, and the chromosomes of the baby suggest that one of the parents may be a carrier.