The answer is "maybe", especially for small projects. Normally the project charter is just a high level estimate of budget, time, and resources with a desired outcome. When this is the format, the various legal documents and contracts are within the scope of the project and the project charter itself is not legally binding.
For many smaller projects (often those that will have a single contract)however, rather than write a separate project charter, the contract and statement of work becomes the project charter. In these cases, if there is a proper contract, the project charter is legally binding.
There is another circumstance. I have seen complex project charters that run for hundreds of pages. The various subsequent contracts write in terms regarding the project charter, in which case the charter may be legally binding, depending upon the agreement in the contract.
To avoid misinterpretation, all contracts (and project charters if they are incorporated by reference into contracts) should at least be reviewed by a legal professional.