Picker cannot accept borderRadius form style

Put your Picker inside a View

<View style={{borderRadius: 10, borderWidth: 1, borderColor: '#bdc3c7', overflow: 'hidden'}}>

and set the width of your Picker as the width of the View.

Use this code. This works for me.

<View
    style={{
    paddingVertical: 8,
    backgroundColor: '#fff',
    borderWidth: 1,
    borderRadius: 20,
}}>
    <Picker style={{height: 24}}>
        <Picker.Item label="Java" value="java" />
        <Picker.Item label="JavaScript" value="js" />
    </Picker>
</View>