Can I delete access log files in nginx. Will it cause an issue

You can remove access.log as root user, or using sudo.

sudo rm /var/log/nginx/access.log

However after deleting it, the file will not be re-created until nginx is re-loaded or re-started. To reload nginx do:

sudo service nginx reload

To re-size the file to 0 bytes, without having to re-load or re-start nginx, use the truncate command:

sudo truncate --size 0 /var/log/nginx/access.log

You should use the standard log rotation utility in Linux to rotate your logs and delete old logs. See man logrotate for more details.