Put the content that needs to be scrolled in a div with overflow: auto. Around that content div put a div with your rounded corners and overflow: hidden.
Now you can see the scroll bar but its outer corners are hidden and
are not disturbing the rounded corners of the outer div.
Example:
// Insert placeholder text
document.querySelector('.inner').innerHTML = 'Text<br>'.repeat(20);
.outer {
width: 150pt;
border: 1px solid red;
border-radius: 15pt;
overflow: hidden;
}
.inner {
height: 200px;
overflow-y: auto;
}
<div class="outer">
<div class="inner">
<!-- lots of text here -->
</div>
</div>