这样的东西可能会起作用：

import React from 'react';
import './Table.css';
import $ from 'jquery';

export default class Table extends React.Component {

  constructor(props) {
    super(props);
    this.containerRef = React.createRef();
    this.interval = null;
    this.scrollIndex = 0;
  }

  componentDidMount() {
    this.startScrolling();
  }

  startScrolling() {
    this.interval = setInterval(() => {
      const container = this.containerRef.current;
      if (container === null) return;
      
      const containerHeight = container.clientHeight;

      const rows = container.querySelectorAll("tr");
      const nChildren = rows.length;
      const rowHeight = rows[0].clientHeight;

      const theadHeight = container.querySelector("thead").clientHeight;

      const nRowsVisible = Math.floor(containerHeight / rowHeight);
      this.scrollIndex = this.scrollIndex + nRowsVisible >= nChildren ?
        0 :
        this.scrollIndex + nRowsVisible

      // Jquery animate is a bit smoother than scrollTo, but either works
      // container.scrollTo({top: this.scrollIndex * rowHeight - theadHeight, behavior: "smooth"});
      $(container).animate({scrollTop: this.scrollIndex * rowHeight - theadHeight}, 1000);
    }, 4000);
  }

  componentWillUnmount() {
    clearInterval(this.interval);
  }

  render() {
    return (
      <div className="tableContainer" ref={this.containerRef}>
        <table className="table table-striped table-dark">
          <thead>
            <tr>
              <th>Table Header</th>
            </tr>
          </thead>
          <tbody>
            <tr><td>row 1</td></tr>
            <tr><td>row 2</td></tr>
            <tr><td>row 3</td></tr>
            <tr><td>row 4</td></tr>
            <tr><td>row 5</td></tr>
            <tr><td>row 6</td></tr>
            <tr><td>row 7</td></tr>
            <tr><td>row 8</td></tr>
          </tbody>
        </table>
      </div>

    )
  }
}

个字符
我有相同的用例，并首先实现了上面的方法。我后来需要一个更连续/循环滚动，我最终实现了w/ CSS动画（实现可以看到here）。
我刚刚发布了一个react组件到npm，如果它可能符合您的需求：react-auto-scroll-table。