It requires the official MaterialCardView (which extends the androidx.cardview.widget.CardView) and at least the version 1.1.0 of the Material components library.
Add to your layout the MaterialCardView:
<com.google.android.material.card.MaterialCardView
style="@style/CustomCardViewStyle"
...>
</com.google.android.material.card.MaterialCardView>
Define a custom style inheriting a material card style (for example Widget.MaterialComponents.CardView) and use the shapeAppearanceOverlay attribute:
<style name="CustomCardViewStyle" parent="@style/Widget.MaterialComponents.CardView">
<item name="shapeAppearanceOverlay">@style/ShapeAppearanceOverlay_card_custom_corners</item>
</style>
<style name="ShapeAppearanceOverlay_card_custom_corners" parent="">
<item name="cornerFamily">rounded</item>
<item name="cornerSizeTopRight">4dp</item>
<item name="cornerSizeTopLeft">8dp</item>
<item name="cornerSizeBottomRight">16dp</item>
<item name="cornerSizeBottomLeft">0dp</item>
</style>

You can also achieve it programmatically.
Just apply a custom ShapeAppearanceModel to the corners of the card.
Something like:
float radius = getResources().getDimension(R.dimen.my_corner_radius);
cardView.setShapeAppearanceModel(
cardView.getShapeAppearanceModel()
.toBuilder()
.setTopLeftCorner(CornerFamily.ROUNDED,..)
.setTopRightCorner(CornerFamily.ROUNDED,..)
.setBottomRightCorner(CornerFamily.ROUNDED,radius)
.setBottomLeftCornerSize(0)
.build());
Note: it requires the version 1.1.0 of the library.
With Jetpack compose you can use the shape parameter in the Card.
Something like:
Card(
shape = RoundedCornerShape(
topStart = 4.dp,
topEnd = 8.dp,
bottomEnd = 16.dp,
bottomStart = 2.dp,
)
){
Text("Content Card")
}
