How do I set the rounded corner radius of a color drawable using xml?

Use the <shape> tag to create a drawable in XML with rounded corners. (You can do other stuff with the shape tag like define a color gradient as well).

Here's a copy of a XML file I'm using in one of my apps to create a drawable with a white background, black border and rounded corners:

<?xml version="1.0" encoding="UTF-8"?> 
<shape xmlns:android="http://schemas.android.com/apk/res/android"> 
    <solid android:color="#ffffffff"/>    
             
    <stroke android:width="3dp"
            android:color="#ff000000" />

    <padding android:left="1dp"
             android:top="1dp"
             android:right="1dp"
             android:bottom="1dp" /> 
             
    <corners android:radius="7dp" /> 
</shape>

mbaird's answer works fine. Just be aware that there seems to be a bug in Android (2.1 at least), that if you set any individual corner's radius to 0, it forces all the corners to 0 (at least that's the case with "dp" units; I didn't try it with any other units).

I needed a shape where the top corners were rounded and the bottom corners were square. I got achieved this by setting the corners I wanted to be square to a value slightly larger than 0: 0.1dp. This still renders as square corners, but it doesn't force the other corners to be 0 radius.

Try below code

<shape xmlns:android="http://schemas.android.com/apk/res/android">
<corners
    android:bottomLeftRadius="30dp"
    android:bottomRightRadius="30dp"
    android:topLeftRadius="30dp"
    android:topRightRadius="30dp" />
<solid android:color="#1271BB" />

<stroke
    android:width="5dp"
    android:color="#1271BB" />

<padding
    android:bottom="1dp"
    android:left="1dp"
    android:right="1dp"
    android:top="1dp" /></shape>