Yes there is. It’s called TextInput, the normal TextInput Component supports multiple lines.
Just assign following properties to your TextInput Component
multiline = {true}
numberOfLines = {4}
At the end you should have this:
<TextInput
multiline={true}
numberOfLines={4}
onChangeText={(text) => this.setState({text})}
value={this.state.text}/>
Source https://facebook.github.io/react-native/docs/textinput