Yes. The Transportation Security Administration (TSA) permits fishing rods in both carry-on and checked bags on flights it screens.
The main limit is size, not security. TSA advises travelers to check with their airline that the rod fits within the carrier’s size limits for carry-on items, because each airline sets its own. Sharp tackle that may be considered dangerous, such as large fish hooks, should be sheathed, securely wrapped, and packed in checked bags. Small fishing lures are allowed in both carry-on and checked bags. TSA also suggests keeping expensive reels or fragile tackle that poses no security threat, such as small flies, in your carry-on, as you would other high-value items. Whatever the general rule says, the final decision on whether an item is allowed through the checkpoint rests with the TSA officer doing the screening.
Source: TSA, What Can I Bring? Fishing pole
Image: Spinning reel on a rod, JaredMcKenzie, CC0, via Wikimedia Commons.