Here's a solution that doesn't require icon fonts or images. This is all the CSS you need:
.dropdown-item-checked::before {
position: absolute;
left: .4rem;
content: '✓';
font-weight: 600;
}
Toggling the Checked State
To add/remove a checkmark, just toggle the dropdown-item-checked modifier on the appropriate dropdown-item:
<div class="dropdown">
<button type="button" class="btn btn-secondary dropdown-toggle" data-toggle="dropdown">Menu</button>
<div class="dropdown-menu">
<a href="#" class="dropdown-item">Item 1</a>
<a href="#" class="dropdown-item dropdown-item-checked">Item 2</a>
<a href="#" class="dropdown-item">Item 3</a>
</div>
</div>
Here's what it looks like:

Demo & Source
Demo: https://codepen.io/claviska/pen/aLxQgv
Source: https://www.abeautifulsite.net/adding-a-checked-state-to-bootstrap-4-dropdown-menus