Can we get a construction loan with a 650 score?

It is very unlikely. A construction loan has more lender risk than a regular mortgage. For instance, if a contractor does not perform or there is some dispute between supplier and the general contractor, the property won't be finished in a timely manner and construction costs will rise. This exerts a lot of risk on the bank holding the construction loan.( They can foreclose on an unfinished home but it would be hard to convert into cash)For this reason most construction loans are give to clients with very high credit scores, good, consistent income, and money in the bank called reserves.

You might find a local credit union or community bank that would do it if your overall qualifications are strong other than the credit score, but expect to need 20-30% downpayment. Good luck!

There is a construction loan offered by a Nationwide Lender and you need to have a 620 FICO to qualify. Use the link I am including to check into this further. Good Luck: https://www.afrwholesale.com/programs/one-time-close.html