Sure! Virtually all lenders who sell mortgages to Fannie Mae or Freddie Mac will be able to offer you a mortgage with a 10-year term. However, interest rates are usually the same as the lender's 15-year fixed-rate offerings.
Since the audience for these shorter-term mortgages is smaller, and although they can offer them, not all lenders will have them on their mortgage menu or in their posted offerings, but at least some will. You can see some current 10-year FRM mortgage offers in the group of lenders posted below. As well, many smaller lenders such as community banks and credit unions like to originate 10-year FRMs and will hold them on their books, so if you like a local aspect to your loan origination and servicing, you might check for offers in your neighborhood market, too.
A term as short as 10 years of course means your monthly payment will be higher than, say, a 15-year term would bring. If you find a great lender you want to work with but they don't offer a 10-year term, you can always make one yourself by refinancing to a 15-year FRM and prepaying your mortgage to create a 10-year term.
Using HSH's It's My Term mortgage prepayment calculator, simply plug in your refinance offer's particulars and choose an end date 10 years from when your loan begins. The calculator will tell you exactly how much you'll need to prepay to have that 10-year term and how much interest you'll save compared with the original term. Start making prepayments from your very first payment, and you'll end up with a 10-year mortgage term.
If you don't want to refinance, but simply want to end your existing mortgage in 10 years' time, the calculator can help you with that, too. As before, add in the particulars of your existing mortgage, select a date 10 years in the future, and calculate how much you'll need to prepay to terminate your loan when you want it to end.
In some cases, such as a mortgage with a small loan balance or of meeting today's underwriting standards for income and documentation might be a challenge, it's technically possible to achieve refinance-like savings without refinancing by prepaying your mortgage. If this might be your situation, you'll want to check out HSH's PreFism Prepayment::Refinance calculator.