Construction of an Armored Fill crossing may be a better option than installing a culvert. Armored Fill crossings work well on low-use roads where ephemeral streams cross the road. If the proper size rock is used and the road is dipped wide enough they have a good capacity to handle large storm events. Another nice feature about Armored Fill crossings is that they wont plug, separate, or rust out like a culverted crossing can.
Check out this video of a successful armored fill crossing.