yes as Reid mentioned via Zapier, Integromat for example. Now it really depends on what you are trying to achieve or what system you have already set up for order dispatch.
If you are selling products that are stored in a warehouse maybe it will work better though if you connect them to their system directly?
Or if you sell handmade products for example that you make and dispatch there are other apps that allow you cheap label printing directly within Shopify.
If connecting to Asana you might also want to first put together a list of what you want to achieve. For example do you want the connection to pull comments from Asana onto the Shopify order page as well or just for new orders to be fetched into Asana and then when a custom field is changed for example to mark the order as dispatched in Shopify.
In our company we use Integromat for example as we figured it allows us to set up a more customized integration.
Also not sure what Shopify Plan you are on but in case you have Pro this might be interesting: Automate across apps with connectors · Shopify Help Center