Not really - the ability to show pop ups to the user (both to just present text and to request input) isn't part of the platform. Please create a new entry in the PowerApps Ideas Board if you feel that this feature is important.
You can, however, simulate a pop-up by "drawing" your pop-up on top of the screen (i.e., a Rectangle shape, a text box to indicate the caption, a text input for the user to enter the value, and a button to confirm the data entry), and set the Visible of those controls to a variable (variables default to false). When you want to show the dialog, you would set that variable to true. Notice that this wouldn't be a modal dialog, so you would need to make the dialog cover the whole screen to prevent the user from interacting with other controls while the dialog is showing.
Here's a more detailed example of how this can be accomplish. For simplicity sake, I'm drawing the dialog not on top of the "trigger" button:
And setting the following properties:
Button1.Text: "Click to open input box"
Button1.OnSelect: UpdateContext({variableDefault:" "});UpdateContext({showDialog:true,variableDefault:""})
TextBox1.Text: "Value entered: " & variable
Rectangle1.Visible: showDialog
TextBox2.Visible: showDialog
TextBox2.Text: "Enter the value:"
TextInput1.Visible: showDialog
TextInput1.Default: variableDefault
ButtonOK.Visible: showDialog
ButtonOK.OnSelect: UpdateContext({showDialog:false,variable:TextInput1.Text})
ButtonCancel.Visible: showDialog
ButtonCancel.OnSelect: UpdateContext({showDialog:false})When clicking the first button, it changes the value of the 'variableDefault' variable to clear the value in the text input from the dialog, and then setting the 'showDialog' to true. When the cancel button is pressed, it only hides the dialog, but when the OK button is pressed, then it also updates the variable value with the text from the input.
