I would like to share some data, i.e shapefile along with the symbology created from open source QGIS tool to ArcGIS.
Can anybody suggest the way forward?
Shapefile is a native ESRI format, so you don't need any process to open it in ArcGIS.
However, there is no real symbology sharing protocol for the symbology, though there are suggestions to use the SLD (QGIS symbology to ESRI).
Depending on your need (sharing the data or a view of the data), you might consider creating a WFS/WMS with your data, which could then be added in ArcGIS with its symbology.