Before FontAwesome 5:
The standard declarations just contain .fa-rotate-90, .fa-rotate-180 and .fa-rotate-270.
However you can easily create your own:
.fa-rotate-45 {
    -webkit-transform: rotate(45deg);
    -moz-transform: rotate(45deg);
    -ms-transform: rotate(45deg);
    -o-transform: rotate(45deg);
    transform: rotate(45deg);
}
With FontAwesome 5:
You can use what’s so called “Power Transforms”. Example:
<i class="fas fa-snowman" data-fa-transform="rotate-90"></i>
<i class="fas fa-snowman" data-fa-transform="rotate-180"></i>
<i class="fas fa-snowman" data-fa-transform="rotate-270"></i>
<i class="fas fa-snowman" data-fa-transform="rotate-30"></i>
<i class="fas fa-snowman" data-fa-transform="rotate--30"></i>
You need to add the data-fa-transform attribute with the value of rotate- and your desired rotation in degrees.
Source: https://fontawesome.com/how-to-use/on-the-web/styling/power-transforms