效果

<template>
  <div class="hello">
    <!-- 拖拽功能必须绑定row-key唯一 -->
    <el-table
      ref="dragTable"
      :data="tableData"
      style="width: 100%"
      row-key="id"
    >
      <el-table-column prop="date" label="日期" width="180"> </el-table-column>
      <el-table-column prop="name" label="姓名" width="180"> </el-table-column>
      <el-table-column prop="address" label="地址"> </el-table-column>
    </el-table>
  </div>
</template>

<script>
import { Table, TableColumn } from 'element-ui'
// 引用第三方拖拽插件
import Sortable from 'sortablejs'
export default {
  name: 'HelloWorld',
  components: {
    ElTable: Table,
    ElTableColumn: TableColumn
  },
  data () {
    return {
      tableData: [
        {
          id: 0,
          date: '2016-05-02',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1518 弄'
        },
        {
          id: 1,
          date: '2016-05-04',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1517 弄'
        },
        {
          id: 2,
          date: '2016-05-01',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1519 弄'
        },
        {
          id: 3,
          date: '2016-05-03',
          name: '王小虎',
          address: '上海市普陀区金沙江路 1516 弄'
        }
      ],
      sortable: null,
      newList: []
    }
  },
  mounted () {
   //这里我是在mounted中调用了拖拽方法，一般获取到表格数据后nextTick中就可以调用拖拽方法
    this.setSort()
  },
  methods: {
    setSort () {
      const el = this.$refs.dragTable.$el.querySelectorAll(
        '.el-table__body-wrapper > table > tbody'
      )[0]
      this.sortable = Sortable.create(el, {
        ghostClass: 'sortable-ghost', 
        setData: function (dataTransfer) {
          dataTransfer.setData('Text', '')
        },
        onEnd: evt => {
          const targetRow = this.tableData.splice(evt.oldIndex, 1)[0]
          this.tableData.splice(evt.newIndex, 0, targetRow)
          const tempIndex = this.newList.splice(evt.oldIndex, 1)[0]
          this.newList.splice(evt.newIndex, 0, tempIndex)
        }
      })
    }
  }
}
</script>

<style>
.sortable-ghost {
  opacity: 0.8;
  color: #fff !important;
  background: #b0c4de !important;
}
</style>

<style scoped>
.icon-star {
  margin-right: 2px;
}
.drag-handler {
  width: 20px;
  height: 20px;
  cursor: pointer;
}
.show-d {
  margin-top: 15px;
}
</style>