I've compiled a short list of potential sources to answer the question:
Any other suggestions, edits, or comments welcome.
I have not found a satisfactory result though I searched a lot. So I have created my own dataset. You can go to this link https://github.com/S-Nakib/Randomly-genrated-Directed-Acyclic-Graph-with-fixed-nodes.-
I have posted it here so that if someone later comes here searching it again.
Here are some good places to look for graph and network datasets
Awesome list by briatte/awesome-network-analysis
Stanford Large Network Dataset Collection
UCI Network Data Repository
ASU Network Datasets
Aminer Datasets for Social Network Analysis
Datasets from the book "Network Science" by Albert-László Barabási
UCINET format datasets