How can I replace the minicart icon when using a custom theme?
Try something like this in your .css:
.minicart-wrapper a.action.showcart::before {
content: "*whatever content you want, for example Font Awesome*";
}
You can also use a background-image
.
Here's how to include CSS in your theme: https://devdocs.magento.com/guides/v2.2/frontend-dev-guide/css-topics/css-themes.html
It depends on your theme. If this is a standard theme(luma), then you need to change the styles in the .css file. For the selector .minicart-wrapper .action.showcart::before
.