Consumers added to their non-mortgage debts for the fourth straight month in January, suggesting that the U.S. economy owes its recent acceleration in part to renewed borrowing.

Consumer credit, which excludes real estate loans such as home mortgages, grew at a 2.5% annual pace to $2.4 trillion, the Federal Reserve said Monday. A nearly 7% increase in non-revolving credit—including loans for autos, boats and education—drove the gains, while credit-card debt fell to a new six-year...