You could use save and load functions or assignin function (if you want to send data from appdesigner to base workspace). But maybe a better approach is to read the data directly in your app, just call it from the startup of your app, putting the table in your app.UITable.
% In your workspace:
save('myFile.mat', 'myTableVariable')
% In your app:
load('myFile.mat')
app.UITable.Data = myTableVariable;
