EDIT :

As correctly pointed by @Bergi, we don't really need to bind the the renderData function, as the state is correctly available to the method. I took the liberty as created a fiddle to check the issues, and it is indeed with the response of the API call.

response.data returns an object but response.data.data is an Array. It is corrected in the fiddle

UNSAFE_componentWillMount() {
   console.log('componentWillMount');
   axios.get('https://reqres.in/api/users')
    .then(response => {  
         this.setState({ data: response.data.data})
     });
}

You need to bind the renderData to the correct lexical scope for react to be able to refer to your component's state defined within. Also, I'd recommend checking your response.data returned from the API call before setting the state.

Other option is to use arrow function renderData = () => {...} but it has a drawback that every instance of your component will get its own copy of this function, thereby increasing its memory footprint.

You can do the following:

import React, {Component} from 'react';
import {View, Text} from 'react-native';
import axios from 'axios'


//servislere bağlanabilmek için class haline getireceğiz
class Liste extends Component {
    constructor(props) {
      super(props);
      this.state = {data: [] };
      this.renderData = this.renderData.bind(this);
    }
    
    UNSAFE_componentWillMount() {
        console.log('componentWillMount');
        axios.get('https://reqres.in/api/users')
        .then(response => { 
            if(response && Array.isArray(response.data)) {
               this.setState({ data: response.data})
            } else {
              // handle the type mismatch here
            }
         });
    }
    componentDidMount() {
        console.log('componentDidMount');
    }

    renderData() {
        return this.state.data.map( responseData => 
            <Text> {responseData.title} </Text>    
        );
    }

    render() {
        console.log('gelen data', this.state);
        console.log('render');
        return (
            <View style={{marginTop: 5}}>
                {this.renderData()}
            </View>
        );
    }
}

export default Liste;