Integer input validation

Code Repetition

In your program, you are using the following code three times:

System.out.print("a: ");
if (!in.hasNextInt() || (a = in.nextInt()) <= 0) {
 System.out.println("Input must be a positive integer!");
 return;
}

You should use a method for this:

public static int getUserInput() {
 Scanner in = new Scanner(System.in);
 int number;
 if (!in.hasNextInt() || (number = in.nextInt()) <= 0) {
  System.out.println("Input must be a positive integer!");
  return -1; //Returns -1 for illegal input
 }
 return number;
}

Input validation

It's good that you control, whether the user made a valid input, but this point can be improved further: Your program stops, when the user makes an invalid input. That's not what an user expects:

public static int getUserInput(String var) {
 Scanner sc = new Scanner(System.in);
 int number;
 while(true) {
  try {
   System.out.print(var + ": ");
   number = sc.nextInt();
   if(number <= 0) {
    throw new InputMismatchException();
   }
   break;  
  } 
  catch(InputMismatchException e) {
   System.out.println("Enter a number > 0.");
   sc.nextLine();
  }
 } 
 return number;
}

By using this code, the user will be able to make inputs until making a valid input. If you don't know about try-catch yet, i suggest reading this explanation.

Logic

I would create a seperate method for the "triangle-validation":

public static boolean isTriangle(int a, int b, int c) {
 if (a + b > c && a + c > b && b + c > a) {
  return true;
 } else {
  return false;
 }
}

Style

Please consider using more than one space for indentation. My suggestion is two or even four spaces. This improves the legibility.

Final code

import java.util.Scanner;
import java.util.InputMismatchException;

public class Triangle {
    public static void main(String[] args) {
        int a, b, c;
        Scanner in = new Scanner(System.in);

        // Prompt for a
        a = getUserInput("a");

        // Prompt for b
        b = getUserInput("b");


        // Prompt for c
        c = getUserInput("c");

        if (isTriangle(a, b, c)) {
            System.out.println("It's a triangle.");
        } else {
            System.out.println("Invalid lengths for a triangle.");
        }
    }

    public static boolean isTriangle(int a, int b, int c) {
        if (a + b > c && a + c > b && b + c > a) {
            return true;
        } else {
            return false;
        }
    }

    public static int getUserInput(String var) {
        Scanner sc = new Scanner(System.in);
        int number;
        while(true) {
            try {
                System.out.print(var + ": ");
                number = sc.nextInt();
                if(number <= 0) {
                    throw new InputMismatchException();
                }
                break;  
            }
            catch(InputMismatchException e) {
                System.out.println("Enter a number > 0.");
                sc.nextLine();
            }
        } 
        return number;
    }
}