I'm not sure which template you are using. If the icon is in a content area, add it first (as you are doing), then select it and add the hyperlink as a second step.
If it is an image object in your template, then the template either has a link field, or the template needs to be modified to accommodate it.
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Sophia - this isn't just limited to social media icons but for any image that's being added in your email. You need to work with your template developer to enable this attribute at the template level. Specifically, the highlighted attribute: