Yes, merchants are allowed to accept credit card payments by phone, and there are various software solutions to enable the process. However, it's important to avoid recording calls, writing down card details, or storing card information. Not doing so may result in data leaks, fraud, PCI/DSS compliance breaches, and other liability issues. Similarly, if your business chooses to accept over-the-phone payments, make sure to employ the proper fraud prevention strategies to avoid card-not-present fraud.