Yes. The Transportation Security Administration (TSA) says crampons are generally permitted in carry-on bags, and they are also allowed in checked bags.
TSA lists crampons with a “Yes (Special Instructions)” rating for carry-on luggage. The special instruction is that TSA officers have the discretion to prohibit an item at the checkpoint if they believe it may pose a security threat, so carry-on approval is not guaranteed. For checked bags, TSA lists crampons as a plain “Yes” with no special conditions. That makes checked luggage the more predictable option for mountaineers and winter hikers who do not want to risk giving up their gear at screening. TSA also notes that the final decision on whether any item is allowed through the checkpoint rests with the officer on duty. This guidance covers TSA security screening at U.S. airports, and TSA last updated its crampons entry on June 25, 2018.
Source: TSA, “What Can I Bring? Crampons”
Image: Crampons on an ice climbing boot, by Dbaisley, public domain, via Wikimedia Commons.